i 





Gass. 
Book. 



THE 



YOUNG MILL-WRIGHT 



MILLER'S GUIDE 



ILLUSTRATED BY 



TWENTY-EIGHT DESCRIPTIVE PLATES. 



OLIVER EVANS. 



$!)£ ftlj'trtunti) (SMtion, 
WITH ADDITIONS AND COKKECTIONS, 



BY THOMAS P. JONES, 

MEMBER OF THE AMERICAN PHILOSOPHICAL SOCIETY, AND LATE PROFESSOR OF 
MECHANICS IN THE FRAN}lLIN„INSTITTJTE OF PHILADELPHIA. 



A DESCRIPTION OF AN IMPROVED MERCHANT FLOUR-MILL. 



2® ft I) jEnflr a hi ngs, 



BY C. & 0. EVANS, ENGINEERS. 




PHILADELPHIA.: 

LEA & BLANCHARD 

1850. 



c- 



It 



<~ . 



Entered, according to the Act of Congress, in the year 1834, by Carey, Lea & 
Blanchard, in the Clerk's Office of the Eastern District of Pennsylvania. 



\ 






WM. S. YOUNG, PRINTER. 



PREFACE. 



There are few men whose mechanical inventions have 
contributed so much to the good of our country as those 
of Oliver Evans; for my own part, I could name but two, 
and they are Whitney and Fulton. There have, it is 
true, within the last thirty years, been a great number 
of original machines invented, and a great man}*- improve- 
ments- made on those for which we are indebted to other 
countries, that do great credit to American genius, and 
evince a peculiar aptitude to excel in mechanical con- 
trivances: but few, however, of these inventions could be 
denominated national, although they have been of high 
importance in the various arts to which they are applied. 

The improvements in the flour mill, like the invention 
of the cotton gin, apply to one of the great staples of our 
country; and, although nearly forty years have elapsed 
since Mr. Evans first made his improvements known to 
the world in the present work, the general superiority of 
American mills to those even of Great Britain, is still a 
subject of remark by intelligent travellers. Mr. Evans, 
however, experienced the fate of most other meritorious 
inventors ; the combined powers of prejudice and of in- 
terest deprived him of all benefit from his labours, and, 
like Whitney, he was compelled to depend upon other 
pursuits for the means of establishing himself in the 
world. His reward, as an inventor, was a long continued 
course of ruinous litigation, and the eventual success of 
the powerful phalanx which was in league against him. 



IV PREFACE. 

It is not the intention of the editor to pronounce a 
panegyric on, or to write the history of, Oliver Evans; 
but his sense of justice, and a confident hope that, in the 
history of American inventions, posterity may accord to 
him the place which he really merits, have called forth 
the preceding remarks. 

Mr. Evans made no pretensions to literature; he con- 
sidered himself, as he really was, a plain, practical man ; 
and the main object of his writing this work was to in- 
troduce his inventions to public notice; it has, however, 
been extensively useful to the mill-wright and the miller, 
as a general treatise, and an edition of it has been pub- 
lished in the French language. The present editor was 
employed to revise the work, a few years ago, and a new 
edition being again called for, the same task has been 
again assigned to him by the publishers. It has not 
been thought proper to make any such alterations in it 
as should destroy its identity; as it would, in that case, 
be essentially a new work, to which it would not be 
proper to attach the name of Mr. Evans as the author; 
encouraged, however, by the general approval of the 
alterations and additions formerly made, the editor has 
thought himself justified in pursuing, in the present in- 
stance, the same course, to a greater extent; and although 
some theoretical views are interwoven in the general 
texture of the work which may be disputable, these can 
detract but little from its practical utility; and it is hoped 
that the farther changes which have been made in the 
phraseology, as well as in some other points, will be 
found to add to its worth in this respect. 

THOMAS P. JONES. 
City of Washington, April, 1834. 



CONTENTS. 



PART I. 



PRINCIPLES OF MECHANICS AND HYDRAULICS. 

ARTICLE PAGE 

1. Preliminary Remarks, - - - - - - 17 

2. On the essential properties of bodies, -.'."- - - - 18 

3. Axioms, or laws of motion and rest, - - - - 21 

4. On absolute and relative motion, - - - - - 22 

5. On Momentum, - - - - - - -23 

6. On power, or force, and on the motive powers, - - - 24 

7. On the effect of collision, or impact, - - - - 24 

8. On compound motion, - - - - - --26 

9. Of non-elasticity, and of fluidity in impingino- bodies, - - 27 

10. Of falling bodies, 29 

11. Of bodies descending inclined planes and curved surfaces, - 33 

12. Of the motion of projectiles, - - - - 34 

13. Of circular motion and central forces, - - - - 35 

14. Of the centres of magnitude, motion and gravity, - 38 

15. Of the mechanical powers, - - - - - 39 

16. Of the lever, - - - - - - - - 40 

17. General rules for computing the power of an engine, - - 41 

18. Of the different kinds of levers, - - - 42 

19. Compound levers, - - - - - - .43 

20. Calculating the poweT of wheel work, - - - 45 

21. Power decreases as motion increases, - - - - 46 

22. No power gained by enlarging undershot water-wheels, 47 

23. No power gained by double gearintr, - - - - 48 

24. Of the pulley, - - - - - - - - 49 

25. Of the wheel and axle, - - - - - - 49 

26. Of the inclined plane, - - - - - - 50 

27. Of the wedge, _.----- 50 

28. Of the screw, - - - - - - - 51 

29. Of the fly- wheel and its use, - - - - - 52 

30. On friction, - - - - - - --53 

31. On the friction of different substances, - - - - 55 

32. Mechanical contrivances to reduce friction, - - - - . 56 

33. Of maximums, - - - - - - -58 

34. Investigation of old theory, - - - - - - 59 

35. New theory doubted, - - - - " 6 ^ 

36. True theory attempted, - - - ■ - - 6a 

37. Scale of experiments, - - - - " ' h Z 

38. Waring's theory, - - - - - - - 67 

39. The same continued, ----- 



Yl CONTENTS. 

ARTICLE PAGE 

40. Doubts respecting it, - - - - - --71 

41. True theory farther sought for, - - - - -72 

42. " " deduced, - - - - - - - 79 

43. Finding the velocity of a wheel, theorem for, - - - 81 

44. Maximum velocity of overshot wheels, - - - - 82 
Table of velocities of do .... 83 
Preliminary remarks on Hydraulics, - - - 87 

45. Of spouting fluids, -------88 

46. Seventh law of spouting fluids demonstrated, - - - - 91 

47. Its accordance with practice shown, - - - - 92 

48. Hydrostatic paradox, - - - - - --95 

49. Practical results of equal pressure, - - - - 96 

50. To find the pressure on a vessel, - - - - - 96 

51. To find the velocity of spouting fluids, - - - - 97 

52. Effect of water under a given head, - - - - - 97 

53. Water applied to act by gravity, - - - - - 99 

54. Principle of overshot mills, - - - - - - 101 

55. Friction of spouting fluids on apertures, .... 104 

56. Pressure of the air on fluids, - - - - - - 105 

57. Ofpumps, - - . - - - - - - 106 

58. Conveying water under valleys and ovej hills, - - - 108 

59. Definite and indefinite quantities of water striking a wheel, - 108 

60. Motion of breast and pitch-back wheels, - - - - 110 

61. Calculating the power of a mill seat, - 113 

62. Theory and practice compared, •• - - - 115 

63. Observations and experiments on mills in practice, - - 119 
Table of the area and power of mill stones, - - - - 125 

64. On canals for conveying water to mills, - 126 

65. On their size and fall, - - - - - - 127 

66. Of air pipes, to prevent trunks from bursting, ... 129 

67. Smeaton's experiments concerning undershot wheels, - - - 130 

68. " " " overshot wheels, - - 147 

69. v" " " wind mills, - - - 155 



PART II. 

OF THE DIFFERENT KINDS OF MILLS. 

70. Of undershot mills, with a table of their proportions and powers, - 161 

71. Of tub-mills, with a similar table, - - - - - 167 

72. Of breast and pitch-back wheels, with a table for them, - - 172 

73. Of overshot wheels, with tables, - - - - 179 

74. Rules and calculations in regulating the motion, - - . - 185 

75. Rules for finding the pitch circles, - - ... jgg 

76. The same subject, with a table, - - - - - 139 

77. Measuring the contents of garners, hoppers, &c, - - - 193 

78. Of the different kinds of gears, and forms of cogs, - 195 

79. Of spur gears, - - - - - - -- 195 

80. Of face gears, - - - - - - - 197 

81. Of bevel gears, - - - - - - - - 199 

82. Of matching wheels to make the cogs wear equally, - - 201 

83. Of rolling screens and fans, - - - - - 202 

84. Of gudgeons, preventing their heating, &c, ... 204 

85. Building mill dams, - - - - - - - 207 

86. Building mill walls. - - - - - - 209 



CONTENTS. yii 

PART III. 

DESCRIPTION OF THE AUTHOR'S IMPROVEMENTS. 

ARTICLE PAGE 

87. General account of the author's improvements, - - - 211 

88. Of the elevator, conveyer, hopper-boy, drill and descender, - 212 

89. Application of the machines in manufacturing flour, - - 216 

90. Elevating grain from ships, <■ 219 

91. A mill for grinding parcels, - - - - . 221 

92. Improved grist mill, ---___ g23 

93. On elevating from ships, &c, by horse power, - - - 225 

94. On the same, by manual power, ----- 226 

95. Particular directions for constructing elevators, &c. - - - 229 

96. Of the meal elevator, ------ 237 

97. " meal conveyer, - - - - - - 239 

98. " grain conveyer, - - - - - -241 

99. " hopper-boy, - - - - - - - 242 

100. " drill, - -. - - - - 244 

101. Utility of these machines, - - - - - - 246 

102. Bills of materials for their construction, - 248 

103. Mills for hulling and cleaning rice, - - - - 251 

PART IV. 

ON THE MANUFACTURING OF GRAIN INTO FLOUR. 

104. Explanation of the principle of grinding, - - - - 255 

105. Of the draught necessary to be given to the furrows of mill-stones, 258 

106. Of facing mill-stones, - - - - - - 262 

107. Of hanging do ..... 263 

108. Of regulating the feed and water, in grinding, - - 266 

109. Rule for judging of good grinding, - - - - 267 

110. Of dressing and sharpening the stones when dull, - - 268 

111. Of the most proper degree of fineness for flour, - - 269 

112. Directions for grinding wheat mixed with garlic, &c, - 270 

113. Of grinding middlings over, &c, - ... 271 

114. Of the quality of mill-stones to suit that of the wheat, - - 275 

115. Of bolting reels and cloths, with directions for bolting and inspect- 

ing floor, - - - - - - -- 277 

116. The duty of the miller, - . - - - - 280 

117. Peculiar accidents by which mills are subject to catch fire, - - 282 

118. Observations on improving mills, - 283 

PART V. 

ELLICOTT'S PLANS FOR BUILDING MILLS. 

Prefatory remarks, - - - - - - 285 

119. Undershot mills, and laying on the water, ... 288 

120. Directions for making forebays, - - - - 289 

121. Principle of undershot mills, ----- 290 

122. Of breast wheels, 293 

123. Of pitch-back wheels, 294 

124. Of overshot wheels, - - - - - - - 294 

125. On the motion of overshot wheels, ... - 295 

126. Of gearing, 296 

127. Diameter of pitch circles, - ----- 297 



Vlll CONTENTS. 

ARTICLE PAGE 

128. Table for overshot mills of different falls, &c. &c, - - - 299 

129. Constructing undershot wheels, ----- 304 

130. Dressing shafts, - - - - - - - 306 

131. Directions for laying out mortises for arms, - 306 

132. " for putting in gudgeons, - - - - 308 

133. Directions for constructing cog-wheels, - - - 309 

134. " for making sills, spurs, and head blocks, - - 311 

135. Of the best time for cutting, and method of seasoning, cogs, - 312 

136. Of shanking, putting in, and dressing off cogs, - - - 312 

137. Of the little cog-wheel and shaft, - - - - - 314 

138. Directions for making wallowers and trundles, - - - 314 

139. " for fixing the head blocks and hanging the wheels, - 315 

140. " for sinking the balance ryne, - - - - 316 

141. " for bridging the spindle. - - - - - 317 

142. " for making the crane and lighter-staff, - - 317 

143. " for making a hoop for the mill-stones, - - 318 

144. " for grinding sand to face the stones, - - - 319 

145. " for laying out the furrows in new stones, - - - 320 

146. " for making a hopper, shoe and feeder, - 321 

147. " for making bolting chests and reels, - - - 322 

148. " for setting bolts to go by water, ... 323 

149. " for making bolting wheels, - - - 324 

150. Of rolling-screens, - ... 326 

151. Offans, 327 

152. Of the shaking sieve, ------ 327 

153. Of the use of draughting to build mills by, - - - - 329 

154. Directions for draughting and planning mills, - 330 

155. Bills of scantling for a mill, - - - - - - 331 

156. Bills of iron work for do ----- 334 

157. Explanation of the plates, - - - - - 336 

158. Of saw-mills, with a table of the dimensions of flutter-wheels, - 340 

159. Of fulling-mills, ------- 348 

160. Management of the saw-mill, - - - - - - 350 

161. Mr. French on saw-mills, &c, - - - - - 352 
Rules for discovering new improvements, - - - - 355 

APPENDIX. 

Description of an improved merchant-mill, ... 365 

On the construction of water-wheels, by W. Parkin, &c, - - 370 

Remarks by the editor, ------ 373 

On the distance which bodies fall, and the velocities acquired in 

consecutive periods of time, with a table, - - 374 
Comparison of different water-wheels, by Mr. Perkins and Mr. 

Manwaring, - - - - - - - 377 

Remarks, by the editor, - - - - - - 379 

EXTRACTS FROM BUCHANAN ON MILL-WORK. 

Strength and durability of the teeth of wheels, - - - 380 

Of arranging the numbers of do - - - 385 

Of making patterns for cast iron, - - - - 386 

Of malleable or wrought iron gudgeons, - - - - 389 

Of the bearings of shafts, - - - - - 390 

On the framing of mill-work, ----- 391 

On reaction wheels, (extracted from Franklin Journal,) - - 392 

Definition of terms, ------ 396 



THE 



YOUNG MILL-WRIGHT 

AND 

MILIEU'S GUIDE. 

PART THE FIRST. 
CHAPTER I. 

MECHANICS. 

Of the General Properties of Bodies, and the first Principles 
of Mechanics. 

ARTICLE 1. 

PRELIMINARY REMARKS. 

Although there are many good, practical workmen 
who are entirely ignorant of the theory of mechanics as 
a science, it will be universally acknowledged that an 
acquaintance with the general properties of matter, and 
the laws of motion would not only be gratifying to every 
intelligent mind, but would introduce a certainty into 
many mechanical operations which would ensure their 
success ; and this is a truth, with the importance of which 
the author of this work was so fully impressed, that he 
devoted a whole chapter to its consideration. The pre- 
sent editor has thought it best to alter and modify the 
original work, but he has been careful not only to retain 
all that appeared to him important in it, but to make such 
additions, and give such an arrangement to the whole, 
as have appeared to him calculated to place the subject? 
of which it treats in a more familiar light. 
2 



18 MECHANICS. [cHAr. I. 

It is only, however, those properties of bodies, and 
those laws of motion, which most intimately concern the 
practical mechanician, that it is thought proper, here, to 
treat at any length, as any thing farther would be entire- 
ly foreign to the object of this work. 



article 2. 

ON THE ESSENTIAL PROPERTIES OF BODIES. 

There are certain properties of bodies which belong 
to matter in all its forms, these are called its essential 
properties, as they are those without which it cannot ex- 
ist; these are Extension, Figure, Impenetrability, Divisi- 
bility, Mobility, Inertia, and Attraction. 

Extension. We become acquainted with the existence 
of matter only by the space which it occupies. We can- 
not conceive of a body without length, breadth, and 
thickness, which are the three dimensions of extension. 
These vary greatly from each other in different bodies; 
and in some they are all equal to each other, as in the 
sphere and the cube. 

Figure, or shape, is the necessary result of extension, 
and constitutes its limits. The business of the machinist 
is to give to various substances those figures, or shapes, 
which shall adapt them to his purpose. 

Impenetrability is that propert}^, by which a body oc- 
cupies a certain space, which cannot, at the same time, 
be occupied by another body. If a nail be driven into 
a piece of wood, it removes a portion of the latter out 
of its way. Water and other fluids may be made to enter 
the pores of wood, but it is manifest that two distinct 
particles of matter cannot exist in the same space with 
each other. 

Divisibility is the susceptibility of matter to be divided 
into any number of parts. If, in conceiving of the minute- 
ness of the particles of matter, we carry the imagination 
to its utmost limits, we must confess that a single parti- 
cle must contain as many halves, quarters, and eighths, as 
the largest masses. We are not to conclude from this, 



CHAP. I.] MECHANICS, 19 

however, that matter is actually infinitely divisible, al- 
though it is mathematically so. It is probable that the 
Creator has formed masses of matter of certain minute 
particles, which are infinitely hard, and incapable, from 
their nature, of mechanical division. 

Mobility is one of those essential properties of matter, 
which form the very foundation of operative mechanics, 
as it is the capability of matter to be moved from the 
place, or space, which it now occupies. No mechanical 
operation, indeed, or any other change, can be effected in 
matter without motion. 

Inertia, or inactivity j is that negative property of mat- 
ter by which it resists every change of state, whether of 
rest or of motion. By this term we mean to express the 
fact that matter is powerless ; that if at rest, it has no- 
thing within itself tending to put it into motion ; and if 
in motion, its own tendency is to continue to move, which 
it would consequently do perpetually, but for those ex- 
traneous resistances to which every thing upon the sur- 
face of the earth is subjected. The term vis inertia, or 
the power of inertia, is altogether objectionable, although 
it is very frequently employed. If inertia were a power 
existing in a body, it must be in some definite quantity, 
capable of being expressed in numbers, and of resisting 
a force less than itself; but it is a fact, that any force im- 
pressed, however small, will move any body, however 
great. 

Attraction is that power which exists in particles or 
in masses of matter, by which they tend to approach 
each other. It has been divided into five kinds; the at- 
traction of Gravitation, of Cohesion or aggregation, of 
Magnetism, of Electricity, and Chemical attraction. It 
is the two former only of these attractions which claim 
particular attention in their relationship to mechanics. 

The attraction of cohesion is that power by which par- 
ticles of matter become united together and form masses. 
We could conceive of the existence of matter without at- 
traction, but it must be in its original constituent parti- 
cles only, unformed into masses; all matter, however, is 
manifestly endowed with this property, and its particles 
are, therefore, capable of being united together. In or- 
der that the attraction of cohesion may be exerted, it is 



20 MECHANICS. [CHAP. I. 

necessary that the particles of matter be in contact with 
each other, as it does not take place at sensible dis- 
tances. By sawing, filing, grinding, and many other 
mechanical operations, we destroy the attraction of co- 
hesion; and this, indeed, is the great object of these pro- 
cesses. In those bodies which are capable of undergo- 
ing fusion, as the metals, we can readily restore this at- 
traction, by subjecting the disintegrated particles to this 
process. 

The attraction of Gravitation is manifested in masses as 
well as in particles of matter, by it all the bodies in na- 
ture tend to approach each other. The sun, the earth, 
the moon, and all the planets, notwithstanding their im- 
mense distances, are subjected to this universal law. A 
stone, or other substance, if unsupported, falls to the 
earth, in consequence of the attraction existing between 
it and the earth. What we call weight, results from 
this attraction, and is the measure of its force or 
power, in different bodies. The weight of a body is the 
sum of the attractive force exerted upon its individual 
particles. A piece of lead, weighing two pounds, con- 
tains twice as many particles as another weighing but 
one pound, and it is therefore drawn to the earth with 
double the force. It might be supposed that, in conse- 
quence of this double quantity of attraction, the piece of 
two pounds would fall with double the velocity of that 
of one pound; but, upon making the experiment, the 
time of their fall will be precisely the same in each. 
This arises from the inertia of matter, by which, when at 
rest, it tends to remain so; and, therefore, to move a 
double quantitjr with the same velocity, must require a 
double force. Gravitation must be considered as act- 
ing equally on each particle, and consequently, there ex- 
ists no reason why a piece weighing two pounds should 
fall with any greater rapidity than would its two halves, 
were it divided. Light bodies, which expose a large 
surface to the air, are retarded in their fall by the resist- 
ance which it presents ; were that removed, a feather 
would fall with the same velocity as a piece of lead. 

This fact is of high importance in practical mechanics, 
as, in the greater number of instances, gravitation is the 



CHAP. I.] MECHANICS. 21 

active agent in moving machines, and in the construction 
of all, it is an element which must enter into the calcula- 
tion of their power. 



article 3. 

AXIOMS, OR LAWS, OF MOTION AND REST. 

1. Every body in a state of rest, will remain so; and 
every body in motion will continue to move in a right 
line, until a change is effected by the agency of some me- 
chanical force. 

2. The change from rest to motion, and from motion 
to rest, is always proportional to the force producing 
these changes. 

3. Action and reaction are always equal, and in direc- 
tions contrary to each other; or, when two bodies act 
upon each other, the forces are always equal, and di- 
rected towards contrary parts. 

The first of these laws, results, necessarily from the 
inertia of matter. The assertion, however, that a body 
in motion would continue to move in a right line, may 
require some illustration. That motion when once com- 
municated would never cease, is fairly inferred from the 
fact that the motion is continued in the exact proportion 
in which the obstruction is diminished. A pendulum 
will vibrate longer in air than in water, and longer still 
in an exhausted receiver, and stops at last in consequence 
of the friction on its points of suspension, and the imper- 
fection of the vacuum. 

When a stone is thrown in a horizontal direction, as 
motion is constantly retarded, it also moves in a curve, 
and eventually falls to the ground. The retardation, in 
this case, is exactly proportioned to the density of the 
air, and the curve in which it moves is the consequence 
of the force of gravity, which is always drawing it to- 
wards the earth : the curve in which it moves is deter- 
mined by this known force, and is precisely proportion- 
ate to it. It necessarily follows, that, if the course of 
retardation, and of deflection were both removed, that the 



22 MECHANICS. [CHAP. I. 

body would continue its course in a right line. The pre- 
ceding remarks may serve to illustrate the second, as well 
as the first law. 

The third law is confirmed by all our observations on 
the motions of the heavenly bodies, and by all our expe- 
riments. If a glass bottle be struck by a hammer, or a 
hammer by a glass bottle, the bottle will in either case be 
broken by the same degree of moving power: were the 
hammer equally fragile with the bottle, both would be 
broken. If a stone be thrown against a pane of glass, the 
glass would be broken and the stone retarded, in exact 
proportion to the resistance offered by the glass. 

To assert the contrary of this law would be to main- 
tain an absurdity; for if action and reaction be not equal, 
one must be greater than the other, which would be to 
say that the effect was greater 'than, or not equal to, the 
cause. 



ARTICLE 4. 

AN ABSOLUTE AND RELATIVE MOTION. 

The idea intended to be conveyed by the term inolion 
is too familiar to require a definition. 

Motion is either absolute or relative. 

Absolute motion is the removal of a bodj r from one part 
of space to another, as the motion of the earth in its 
orbit. 

Relative motion is the change of place which one body 
undergoes in relationship to another: such, for example, 
as the difference of motion in the flight of two birds, or 
the sailing of two ships. 

. Were all the articles upon the surface of the earth to 
retain their respective situations, they would still be in 
absolute motion with the earth in space, but they would 
experience no relative motion, and would appear to us to 
be at rest. 

In the theory of mechanics, much information is de- 
rived from our knowledge of the laws observed by the 
heavenly bodies in their absolute motions; but, in prac- 



CHAP. I.] MECHANICS, 23 

tical mechanics, we have to do with relative motion 
only. 

On equable, accelerated, and retarded motion. 

Time must, of necessity, enter into the idea of motion, 
as it is the measure of its velocity. Thus a body which 
passes the distance of two miles in an hour, moves with 
twice the velocity of another, which, in the same time, 
travels but one mile. 

A body in motion may continue to move with the same 
velocity throughout its whole course ; its motion is then 
said to be equable: or, 

Its motion may be perpetually increasing, as is the 
case with falling bodies. This is denominated accelerated 
motion. 

Retarded motion, is that which is continually decreasing; 
such is the motion of a stone, or of a cannon ball, pro- 
jected perpendicularly upwards. 

The cause of the equable acceleration of falling bodies, 
and the retardation of such as are projected upwards from 
the earth, will be rendered clear, by attending to the arti- 
cle on falling bodies. 



ARTICLE 5. 

OF MOMENTUM. 

It is known to every one that if the velocity of a moving 
body be increased, the force with which it will strike 
against another body will be increased also : the fact is 
equally familiar, that if the weight of a body in motion 
be increased, the result will be similar. It is evident, 
therefore, that the force with which a body in motion 
strikes against another body, must be in the compound 
ratio of its velocity, and its mass or quantity of matter. 
This force is called its momentum, which is the product 
of its quantity of mailer multiplied by its quantity of 
motion; or, in other words, its weight multiplied by its 
velocity. 



24 MECHANICS. [CHAP. I. 

The effects produced by the collision of bodies against 
each other differ greatly in those which are elastic, from 
those that are non-elastic, which will be more particular- 
ly noticed presently. 



article 6. 

ON POWER, OR FORCE, AND ON THE MOTIVE POWERS. 

Force, or power, in a mechanical sense, is that which 
causes a change in the state of a body, from motion to 
rest, or from rest to motion. 

When two or more forces act upon a body, in such a 
way as to destroy the operation of each other, there is 
then said to be an equilibrium of forces. 

The Motive Powers, are those which we employ to 
produce motion in machines ; these are, the strength of 
men, and of other animals; the descent of weights; the 
force of water in motion; wind, or the motion of the air; 
the elasticity of springs, and the elastic force of steam. 
The whole of these are included in the two principles of 
Gravitation and Elasticity. 

Attempts have been made to employ other agents as 
motive powers, but these have either failed altogether, or 
have not been attended with that success which justifies 
the giving to them a place in a practical work. Among 
these may be mentioned magnetism; electricity; con- 
densed air; air rendered more elastic by heating it; ex- 
plosive gases and fulminating compounds. 



article 7. 

ON THE EFFECTS OF COLLISION, OR IMPACT. 

The striking of bodies against each other is denomi- 
nated collision, or impact. 

Bodies are divided into elastic, and non-elastic. By 
elastic bodies are intended those which resume their di- 



CHAP. I.] MECHANICS. 25 

mensions and form, when the force which changes them 
is removed. Non-elastic bodies are those which not only 
change their forms when struck, but remain permanently 
altered in this particular. Although there are no solid 
bodies which possess either of these properties in perfec- 
tion, yet the difference between those which are most, and 
those which are least elastic, is sufficiently great to justify 
the division. 

Ivory and hardened steel are eminently elastic. Such 
bodies, when struck together, become flattened at the 
point of contact; but immediately resuming their form, 
they react upon each other, and rebound. Lead and soft 
clay are non-elastic: if two balls of either of these 
substances be struck together, a permanent flattening is 
produced at their points of contact, and they do not re- 
bound. 

If two non-elastic bodies, A and B, fig. 1, each having 
the same quantity of matter, move towards each other with 
equal velocities, they will come into contact, as at A B, 
in the centre, where they will remain at rest after the 
stroke, because their momentums were equal, and in op- 
posite directions. That is, if each have two pounds of 
matter, and a velocity which we may call ten, the mo- 
mentum of each is twenty; and just sufficient, therefore, 
to destroy each other. 

If, on the contrary, the bodies be perfectly elastic, they 
will recede from each other with the same velocity with 
which they met. In the former case, a permanent inden- 
tation was produced on the bodies; in the present the flat- 
tening is instantaneous only, and the particles resuming 
their former position and arrangement, react upon each 
other with a force equal to their action, and, after the 
stroke, recede with undiminished velocity. 

If two non-elastic bodies, A and B, fig. 2, moving in 
the same direction with different velocities, impinge upon 
each other, they will move on together after the stroke 
with such velocity as being multiplied into the sum of 
their weights, will produce the sum of the momentums 
which they had before the stroke ; that is, if each weigh 
one pound, and A has 3, and B 4 degrees of velocity, 
the sum of their momentum is 12; 1x8 + 1x4 = 12: 



26 MECHANICS. [CHAP. I. 

then after the stroke their velocity will be 6 ; which, 
multiplied into their quantity of matter 2, produces 12. 
The quantity of motion before and after the stroke, or, 
which is the same thing, their momentums, will be un- 
changed. 

If, on the contrary, they had both been elastic, and 
moving as before, then, after the stroke, A would have 
moved with four, and B with eight degrees of velocity: 
they would consequently have interchanged velocities, 
but the quantity of motion would remain unchanged. 

If A and B be non-elastic bodies, equal in quantity of 
matter, and A moving with a velocity 10, come into con- 
tact with B at rest, they will move on together with the 
velocity 5. The quantity of motion will therefore remain 
unchanged, a double mass moving with one half the ve- 
locity. If the bodies A and B be both elastic, B, after 
the stroke will fly off with the velocity 10, and A will 
remain at rest. The quantity of motion will, as before, 
remain unchanged. To understand this difference be- 
tween elastic and non-elastic bodies, we may suppose 
that when the two elastic bodies come into contact with 
each other, they tend to move on together, like the non- 
elastic, with one half the velocity of the body A; that is, 
A gives half its motion to B ; but being elastic, the im- 
pinging parts, which give way, instantaneously resume 
their form, and react upon each other with a force equal 
to their first action, which drives A back with a velocity 
5, and B forward with an equal velocity: the effect of 
which must be to leave A at rest, and to accumulate the 
whole motion in B. 



ARTICLE O. 

ON COMPOUND MOTION. 

If a body be struck by two equal forces, in contrary 
directions, it will remain unmoved; but if the forces, in- 
stead of acting on the body in directions exactly oppo- 
site, strike it in two directions inclined to each other, 
motion will be communicated to the body so struck ; but 
its direction will not be that of either of the striking bo- 



CHAP. I.] MECHANICS. 27 

dies, but somewhere between them, dependent upon the 
power of the blows respectively. The motion in this 
case is manifestly compounded of the two possessed by 
the striking bodies, and is therefore called a compound 
motion. 

If a body A, fig. 4, receive two strokes, or impulses 
at the same time, in different directions, one which would 
propel it from A to B in a given time, and another which 
would propel it from A to D in an equal time, then 
this compound force will propel it from A to C, in the 
same time in which it would have arrived at B or D by 
one impulse only. If lines be drawn from C, to join B, 
and D, the parallelogram A B C D, will be formed, in 
the diagonal of which the compound motion was per- 
formed. If the two impulses had been equal, then A D 
would be equal to A B, and the parallelogram would be- 
come a square. 

article 9. 

. OF NON-ELASTICITY, AND OF FLUIDITY, IN IMPINGING BODIES. 

If A and B, fig. 3, be two columns of matter in mo- 
tion, meeting each other, and equal in non-elasticity, 
quantity and velocity, they will meet at the dotted line 
e e, destroy each other's motion, and remain at rest, pro- 
vided none of their parts separate. 

But if A be elastic, and B non-elastic, when they meet 
at e e, B will give way by battering up, and both will 
move a little farther; that is, half the distance that B 
shortens. 

But if B be a column of fluid, and when it strikes A, 
flies off in a lateral direction, perpendicular to A, then 
whatever is the sum total of the momentums of these par- 
ticles laterally, has not been communicated to A. 

But with what proportion of the striking velocity the 
fluid, after the stroke, will move in the lateral direction, 
I do not find determined; but, from some experiments I 
have made, I suppose it to be more than one half; be- 
cause water falling four feet, and striking a horizontal 
plane with 16,2 feet velocity will cast some kw drops to 
the distance of 9 feet (say 10 feet, allowing one foot to 



28 MECHANICS. [CHAP. I. 

be lost by friction, &c.) which we must suppose take 
their direction at an angle of 45 degrees ; because a body 
projected at an angle of 45 degrees, will describe the 
greatest possible horizontal range. It is known also, that 
a body falling 4 feet and reflected with its acquired ve- 
locity 16,2 feet at 45 degrees, will reach 16 feet hori- 
zontal range, or four times the distance of the fall. There- 
fore, by this rule | of 10 feet, equal to 2,5 feet, is the fall 
that will produce the velocity necessary to this effect, viz. 
velocity 12,64 feet per second, about three quarters of 
the striking velocity. 

This side force cannot be applied to produce any far- 
ther forward force, after it has struck the first obstacle, 
because its action and reaction then balance each other; 
which I demonstrated by fig. 27. 

Let A be an obstacle, against which the column of 
water G A, of quantity 16 with velocity per second 16, 
strikes ; as it strikes A, suppose it to change its direction 
at right angles with | velocity and to strike B B, then 
to change again and strike forward against C C, and back- 
wards against D D ; then again in the side direction 
E E; and again in the forward and backward directions, 
all of which forces counteract and balance each other. 

Therefore, if we suppose the obstacle A to be the float 
of an undershot water-wheel, the water can be of no far- 
ther service in propelling it, after the first impulse, but 
rather a disadvantage; because the elasticity of the float 
will cause it to rebound in a certain degree, and, instead 
of keeping fully up with the float it struck, to react back 
against the next float. It will be better, therefore, to let 
it escape freely as soon as it has fully made the stroke: 
not sooner, however, as it will require a certain space to 
act in, which will be in direct proportion to the distance 
between the floats. 

From these considerations, we may conclude, that the 
greatest effect to be obtained from striking fluids, will not 
amount to more than half the power which gives them 
motion, and much less, if they be not applied to the best 
advantage: and also that the effect produced by the col- 
lision of non-elastic bodies, will be in proportion to their 
non-elasticity. 



CHAP. I.] MECHANICS. 29 

ARTICLE 10. 
OF FALLING BODIES. 

Bodies descending freely by their gravity, in vacuo, or 
in a non-resisting medium, are subject to the following 
laws : — 

1st. They are equally accelerated. 

It is evident, that, in every equal part of time, the body 
must receive an equal impulse from gravity, which will 
propel it at an equal distance, and give it an equal addi- 
tional velocity; it will, therefore, produce equal effects in 
equal times ; and the velocity will be proportioned to the 
time. 

2d. Their velocity is always in proportion to the time 
of their fall, and the time is as the square root of the dis- 
tance fallen. 

If the velocity, at the end of one second, be 32,4 feet, 
at the end of two seconds, it will be 64,8 ; at the end of 
three seconds, 97,2 feet per second, and so on. 

3d. The spaces through which they pass are as the 
squares of the times and the velocities. 

That is, as the square of one second is to the space 
passed through, 16,2, so is the square of two seconds, 
which is 4, to 64,8 feet, passed through at the end of 2 
seconds ; and so on, for any number of seconds. There- 
fore the spaces passed through at the end of every second 
will be as the square numbers 1, 4, 9, 16, 25, 36, &c, and 
the spaces passed through, in each second separately, 
, will be as the odd numbers 1, 3, 5, 7, 9, 11, 13, 15, &c. 

4th. Their velocities are as the square root of the space 
descended through, and their force, to produce effect, as 
their distances fallen, directly. 

That is, as the square root of 4, which is 2, is to 16,2, 
the velocity acquired in falling four feet ; so is the square 
root of any other distance, to the velocity acquired in fall- 
ing that distance. 

5th. The space passed through the first second, is very 
nearly 16,2 feet, and the velocity acquired, at the lowest 
point, is 32,4 feet, per second. 

6th. A body will pass through twice the space, in a 
horizontal direction, with the last acquired velocity of 



30 MECHANICS. [CHAP. I. 

the descending body, in the same time that its fall re- 
quired. 

That is, suppose the body, as it arrives at the lowest 
point of its fall, and has acquired its greatest velocity, 
were to be turned in a horizontal direction, or that the ac- 
celeration from gravity was at that moment to cease, and 
the velocity to continue uniform, it would then pass over 
double the distance that it had descended through, in the 
same time. 

7th. The total sum of the effective impulse acting on 
falling bodies to give them velocity, is in direct propor- 
tion to the space descended through ;* and their velocity 
being as the square root of the space descended through, 
or, which is the same, as the square root of the total im- 
pulse. Therefore, 

8th. Their momentums, or force to produce effects, 
are as the squares of their velocities,f or directly as their 
distances fallen through ; and the times expended in pro- 
ducing the effects are as the square root of the distance 
fallen through. 

That is, if a body fall 16 feet, and strike a non-elastic 
body, such as soft lead, clay, &c, it will strike with ve- 
locity 32, and produce a certain effect in a certain time. 
Again, if it fall 64 feet, it will strike with velocity 64, and 
produce a quadruple effect, in a double time ; because if 
a perfectly elastic body fall 16 feet (in one second of time, 
and strike a perfectly elastic plane, with velocity 32 feet,) 
it will rise 16 feet in one second of time. Again, if the 
body fall two seconds.„of time, it will fall 64 feet, and 
strike with velocity 64, and rise 64 feet in two seconds 
of time. Now, if we call the rising of the body the effect 
of the striking velocity (which it really is) then all will 
appear clear. I am aware that any thing here advanced, 
which is contrary to the opinion of learned and ingenious 
authors, ought to be doubted, unless found to agree with 
practice. 

* This is evident from the consideration that in every equal part of distance it 
descends through, it receives an equally effective impulse from gravity. There- 
fore, 4 times the distance gives 4 times the effective impulse. 

f This is evident, when we consider that a quadruple distance, or impulse, pro- 
duces only double velocity, and that a quadruple resistance will be required to 
stop double velocity ; consequently, their force is as the squares of their velocities, 
which brings them to be directly as their distances descended through: and this 
agrees with the second law of spouting fluids, Art. 45. e 



CHAP. I.] 



MECHANICS. 



31 



A TABLE 

OF THE 

MOTION OF FALLING BODIES. 

"SUPPOSED IN VACUO, 





>i vf 


G3 


«c tt 


.', <« — 


to 

3 
o 


•"^2 O 


"3 


^u8 

3 w 


^ a 

-C.5 


O ca 

^"2 r. 




a S3 o 


« <" 




O w 


T3 
CD 

xn 


O" * in 

« s =- 


03 05 

a 

■2 Q* 


ra oT 
rt 05 


03 03 r-T 


a. 


•3 •■»" ^ 


™ 


^ s 


Ph« 03 i 


8 "S 


=2 £ 
*• s 3 • 

j3£ 8 


„-S bo 

STj- 
OO-5 

03 


8"S &, 
.1-3 S 


■s-f.S S -o 

s > c 
-53 a- ca 


s 


H 


02 


5 


> 


1 


8.1 


.125 


.25 


4. 


o 


11.4 


.25 


1.01 


8.1 


3 


14. 


.5 


4.05 


16.2 


4 


16.2 


.75 


9.11 


24.3 


5 


18. 


1 


16.2 


32.4 


6 


19.84 


2 


648 


64.8 


7 


21.43 


3 


145.8 


•97.2 


8 


22.8 


4 


259.2 


129.6 


9 


24.3 


5 


305. 


162. 


10 


25.54 


6 


583.2 


194.4 


11 


2673 


7 


793.8 


226.8 


12 


28. 


8 


1036.8 


259.2 


13 


29.16 


9 


1312.2 


291.6 


14 


30.2 


10 


1620. 


324. 


15 


31.34 


30 


14580. 


972. 


16 


32.4 


60 


58320. 


1944. 


17 


33.32 








18 


34.34 








19 


35.18 








20 


36.2 








21 


37.1 L 








36 


48.6 








49 


56.7 








64 


64.8 








100 


81. 








144 


97.2 









32 



MECHANICS. 



[chap. I. 



A SCALE OF THE MOTION OF FALLING BODIES. 



In this table the time is divided into 
seconds, and the absolute distances are 
proportioned to this division ; bin the 
rations are the same, whether minutes, 
hjurs, or any other period, be taken 
as the unit of time. 






<2 a 



03 



= «"_ 
O CS p 

< : 



.1 



Velocity in feet, acquired at the end 
of 1"= 32.4 feet. 



Velocity acquired at the end of 2"= 
64.8 feet. 



8 

V . . 9 - 

10 

11 

12 

13 

14 

I 
1 
15 

4". . 16- 



Velocity acquired at the end of 3"= 
97.2 feet. 



Velocity acquired at the end of 4": 
129.6 feet. 



feet. 
16.2 



64. 



145.8 



259.2 



CHAP. I.] MECHANICS. 33 

This scale shows at one view all the laws observed by 
falling bodies. The body O would fall from O to 1, equal 
to 16,2 feet, in the first second, and acquire a velocity 
that would carry it 32,4 feet from I to a, horizontally, 
in the next second, by laws 5 and 6; this velocity would 
also carry it down to three in the same time; but its gra- 
vity, producing equal effects, in equal times, will acce- 
lerate it so much as to take it to 4 in the same time, by 
law 1. It will now have a velocity of 64,8 feet per se- 
cond, that will take it to b horizontally, or down to 8, 
but gravity will help it on to 9 in the same time. Its 
velocity Will now be 97,2 feet ; which will take it hori- 
zontally to c or down to 15, but gravity will help it on 
to 16; and its last acquired velocity will be 129,6 feet, 
per second, which would carry it to d horizontally. 

If either of these horizontal velocities be continued, 
the body will pass over double the distance it fell, in the 
same time, by law 6. 

Again, if O be perfectly elastic, and falling, strikes a 
perfectly elastic plane, either at 1, 3, 5, or 7, the effec- 
tive force of its stroke will cause it to rise again to O in 
the same space of time it took to fall. 

This shows, that in every equal part of distance, it 
received an equally effective impulse from gravity, and 
that the total sum of the effective impulse is as the dis- 
tance fallen directly — and the effective force of the 
stroke will be as the squares of the velocities, by laws 7 
and 8. 



ARTICLE 11. 
OF BODIES DESCENDING INCLINED PLANES AND CURVED SURFACES. 

Bodies descending inclined planes and curved sur- 
faces, are subject to the following laws: — 

1. They are equably accelerated, because their motion 
is the effect of gravity. 

2. The force of gravity propelling the body A, fig. 5, 
to descend an inclined plane A D, is to the absolute gra- 

3 



34 MECHANICS. [CHAP. I, 

vity of the body as the height of the plane A C is to it3 
length A D. 

3. The spaces descended through are as the squares 
of the times. 

4. The times in which the different planes A D, A H, 
and A I, or the altitude A C, are passed over, are as their 
lengths respectively. 

5. The velocities acquired in descending such planes, 
in the lowest points, D, H, I, or C, are all equal. 

6. The times and velocities of bodies descending 
through planes alike inclined to the horizon, are as the 
square roots of their lengths. 

7. Their velocities, in all cases, are as the square roots 
of their perpendicular descent. 

From these laws or properties of bodies descending 
inclined planes, are deduced the following corollaries : 
namely : — 

1. That the times in which a body descends through 
the diameter A C, or any chord A a, A e, or A i, are 
equal: hence, 

2. All the chords of a circle are described in equal 
times. 

3. The velocity acquired in descending through any 
arcfi, or chord of an arch, of a circle, as at C, in the 
lowest point C, is equal to the velocity that would be ac- 
quired in falling through the perpendicular height F C. 

Pendulums in motion have the same properties, the 
rod or string acting as the smooth, curved surface. 

For illustrations of these properties, see Kater and 
Lardner's Mechanics, p. 79, or any general treatise on 
that subject. 



article 12. 

ON THE MOTION OF PROJECTILES. 

A projectile is a body thrown, or projected, in any di- 
rection ; such as a stone from the hand, water spouting 
from any vessel, a ball from a cannon, &c, fig. 6. 



CHAP. I.] MECHANICS. 35 

Every projectile is acted upon by two forces at the 
same time; namely, Impulse and Gravity. 

By impulse or the projectile force the body will pass 
over equal distances, A B, B C, &c, in equal times by 
1st general law of motion, Art. 7, and by gravity, it de- 
scends through the spaces A G, G H, &c, which are as 
the squares of the times, by 3d law of falling bodies, Art. 
9. Therefore, by these forces compounded, the body will 
describe the curve A Q, called a parabola; and this will 
be the case in all, except perpendicular directions; the 
curve will vary with the elevation, yet it will still be what 
is called a parabola. 

If the body be projected at an angle of 45 degrees ele- 
vation, it will be thrown to the greatest horizontal dis- 
tance possible; and if projected with double velocity, it 
will describe a quadruple range. 



article 13. 

OF CIRCULAR MOTION AND CENTRAL FORCES. 

If a body A, fig. 7, be suspended by a string A C, and 
caused to move round the centre C, that tendency which 
it has to fly from the centre, is called the centrifugal 
force; and the action upon a body; which constantly so- 
licits it towards a centre, is called the centripetal force. 
This is represented by the string, which keeps the body 
A, in the circle A M. Speaking of these two forces in- 
differently, they are called central forces.* 

The particular laws of this species of motion, are, 

1. Equal bodies describing equal circles in equal times, 
have equal central forces. 

2. Unequal bodies describing equal circles in unequal 
times, their central forces are as their quantities of mat- 
ter multiplied into their velocities. 

* It may be well to observe here, that this central force is no real power, hut 
only an effect of the power that gives motion to the body. Its inertia causes it 
to recede from the centre, and fly off in a direct tangent, with the circle it moves 
in; therefore, this central force can neither add to, nor diminish, the power of 
any mechanical or hydraulic engine unless it be by friction and inertia, where 
water is the moving power, and the machine changes its direction. 



36 MECHANICS. [CHAP. I. 

3. Equal bodies describing unequal circles in equal 
times, their velocities and central forces are as their dis- 
tances from their centres of motion, or as the radii of 
their circles.* 

4. Unequal bodies describing unequal circles in equal 
times, their central forces are as their quantities of matter 
multiplied into their distances from their centres, or the 
radii of their circles. 

5. Equal bodies describing equal circles in unequal 
times, their central forces are as the squares of their ve- 
locities; or, in other words, a double velocity generates 
a quadruple central force.f Therefore, 

6. Unequal bodies describing equal circles in unequal 
times, their central forces are as their quantities multi- 
plied into their velocities. 

7. Equal bodies describing unequal circles with equal 
celerities, their central forces are inversely as their dis- 
tances from their centres of motion, or the radii of their 
circles.^ 

* This shows that when mill-stones are of unequal diameters, and revolve in 
equal times, the largest should have the draught of their furrows less, in propor- 
tion as their central force is more; which is in inverse proportion; also, that the 
draught of a stone should vary, and be in inverse proportion to the distance from 
the centre. That is, the greater the distance, the less the draught. 

Hence, we conclude, that if stones revolve in equal times, their draught must 
be equal near the centre ; that is, so much of the large stones as is equal to the 
size of the small ones, must be of equal draught. But that part which is greater 
must have less draught in inverse proportion ; as the distance from the centre is 
greater, the furrows must cross at so much less angle, which will be nearly the 
case (if their furrows lead to an equal distance from their centres) at any conside- 
rable distance from the centre of the stone; but near the centre the angles become 
greater than the proportion; if the furrows be straight, as appears by the lines, 
g 1, h 1, g 2, h 2, g 3, h 3, in fig. 1, PI. XI. the angles near the centre are too 
great, which seems to indicate that the furrows of mill-stones should not be straight, 
but a little curved ; but what this curve should be, is very difficult to lay down 
exactly in practice. By theory it should be such as to cause the angle of furrows 
crossing, to change in inverse proportion with the distance from the centre, which 
will require the furrows to curve more as they approach the centre. 

f This shows that mill-stones of equal diameters, having their velocities une- 
qual, should have the draught of their furrows as the square roots of their number 
of revolutions per minute. Thus, suppose the revolutions of one stone, the fur- 
rows of which are correctly made, to be 81 per minute, and the mean draught of 
the furrows 5 inches, and found to be right, the revolutions of the other stone to 
be 100 ; then, to find the draught, say as the square root of SI, which is 9, is to the 
5 inches, draught, so is the square root of 100, which is 10, to 4,5 inches, the draught 
required (by inverse proportion,) because the draught must decrease as the cen- 
tral force increases. 

i That is, the greater the distance, the less the central force. This shows that 
mill-stones of different diameters, having their peripheries revolving with equal 
velocities, should have the angle of draught, with which their furrows cross each 
other, in inverse proportion to their diameters, because their central forces are as 



CHAP. I.] MECHANICS. 37 

8. Equal bodies describing unequal circles, having 
tbeir central forces equal; their periodical times are as 
the square roots of their distances. 

9. Therefore the squares of the periodical times are 
proportional to the cubes of their distances, when neither 
the periodical times nor the celerities are given. In that 
case, 

10. The central forces are as the squares of the dis- 
tances inversely.* 

their diameters, by inverse proporlion, directly; and the angle of draught should 
increase, as the central force decreases, and decrease, as it increases. 

But here we must consider, that, to give stones of different diameters equal 
draughts, the distance of their furrows from the centre, must be in direct propor- 
tion to their diameters. Thus, as 4 feet diameter is to 4 inches draught, so is 5 
feet diameter to 5 inches draught. To make the furrows of each pair of slones 
cross each other at equal angles, in all proportional distances from the centre, see 
fig. 1, Plate XI. where g b, g d, g f, h a, h c, and h e, show the direction of the 
furrows of the 4, 5, and 6 feet stones, with their proportional draughts; now it is 
obvious that they cross each other at equal angles, because the respective lines 
are parallel, and cross in each stone near the middle of the radius ; which shows 
that in all proportional distances, they cross at equal angles, consequently their 
draughts are equal. 

But the draught must be farther increased with the diameter of the stone, in order 
to increase the angle of draught in the inverse ratio, as the central force decreases. 

To do which, say, — If the 4 feet stone has central force equal 1, what central 
force will the 5 feet stone have? Answer: 8, by the 7th law. 

Then say, — If the central force 1 require 5 inches draught, for a o feet stone, 
what will central force 8 require; Answer: 6.25 inches draught. This is, sup- 
posing the verge of each stone to move with equal velocity. This rule may 
bring out the draught nearly true, provided there be not much difference between 
the diameter of the stones. But it appears to me, that neither the angle wiih 
which the furrows cross, nor the distance of the point from the centre, to which 
they direct, is a true measure of the draught. 

* These are the laws of circular motion and central forces. For experimental 
demonstrations of them, see Ferguson's Lectures on Mechanics, page 27 to 47. 

I may here observe that the whole planetary system is governed by these laws 
of circular motion and central forces. Gravity acting as the string, is the cen- 
tripetal force ; and as the power of gravity decreases, as the square of the distance 
increases, and as the centripetal and centrifugal forces must always be equal in 
order to keep the body in a circle; hence appears the reason why the planets 
most remote from the sun have their motion so slow, while those near him have 
their motions swift; because their celerities must be such as to create a cen- 
trifugal force equal to the attraction of gravity. 



38 MECHANICS. [CHAP. I. 

ARTICLE 14. 

OF THE CENTRES OF MAGNITUDE, MOTION, AND GRAVITY. 

1. The centre of magnitude is that point which is 
equally distant from all the external parts of a body. 

2. The centre of motion is that point which remains 
at rest, while all other parts of the body move round it. 

3. The centre of gravity of bodies, is of great conse- 
quence to be well understood, it being the principle of 
much mechanical motion; it possesses the following par- 
ticular properties. 

1 . If a body b% suspended on this point, as its centre 
of motion, it will remain at re£t in any position. 

2. If a body be suspended on any other point than its 
centre of gravity, it can rest only in such position, that a 
right line drawn from the centre of the earth through the 
centre of gravity will intersect the point of suspension. 

3. When this point is supported, the whole body is 
kept from falling. 

4. When this point is at liberty to descend in a right 
line; the whole body will fall. 

5. The centre of gravity of all homogeneal bodies, as 
squares, circles, spheres, &c, is the middle point in a 
line connecting any two opposite points or angles. 

6. In a triangle, it is in a right line drawn ;from any 
angle to bisect the opposite side, and at the distance of 
one-third of its length from the side bisected. 

7. In a hollow cone, it is in a right line passing from 
the apex to the centre of the base, and at the distance of 
one-third of the side from the base. 

8. In a solid cone, it is one-fourth of the side from the 
base, in a line drawn from the apex to the centre of the 
base. 

The solution of many curious phenomena, as, why 
many bodies stand more firmly on their bases than others; 
and why some bodies lean considerably over without fall- 
ing, depends upon a knowledge of the position of the cen- 
tre of gravity. 

Hence appears the reason, why wheel-carriages, load- 



CHAP. II.] MECHANICS. 39 

ed with stones, iron, or any heavy matter, will not over- 
turn so easily, as when loaded with wood, hay, or any 
light article; for when the load is not higher than a b, 
fig. 22, a line from the centre of gravity will fall within 
the centre of the base at c ; but if the load be as high as 
d, it will then fall outside the base of the wheels at e, 
consequently it will overturn. From this appears the 
error of those, who hastily rise in a coach or boat, when it 
is likely to overset, thereby throwing the centre of gravi- 
ty more out of the base, and increasing their danger. 



CHAPTER II. 



ARTICLE 15. 
OF THE MECHANICAL POWER. 

Having premised and considered all that is necessary 
for the better understanding those machines called me- 
chanical powers, we now proceed to treat of them. They 
are six in number; namely: 

The Lever, the Pulley, the Wheel and Axle, the In- 
clined Plane, and the Screw. 

These are called Mechanical Powers, because they in- 
crease our power of raising or moving heavy bodies. Al- 
though they are six in number, yet they are all governed 
by one simple principle, which I shall call the first Gene- 
ral Law of Mechanical Powers ; it is this, the momentams 
of the power and weight are always equal, when the engine 
is in equilibrio. 

Momentum, here means the product of the weight of 
the body multiplied into the distance it moves; that is, 
the power multiplied into its distance moved, or into its 
distance from the centre of motion, or into its velocity, 
is equal to the weight multiplied into its distance moved, 
or into its distance from the centre of motion, or into its 
velocity; or, the power multiplied into its perpendicular 
descent, is equal to the weight multiplied into its perpen- 
dicular ascent. 



40 MECHANICS. [CHAP. II. 

The Second General Law of Mechanical Powers, is, 

The power of the engine, and velocity of the weight moved 
are always in the inverse proportion to each other ; that is, 
the greater the velocity of the weight moved, the less it 
must be; and the less the velocity the greater the weight 
may be: and that universally in all cases. 

The Third General Law, is, 

Part of the original power is always lost in overcoming 
friction, inertia, SfC, bid no power can be gained by engines, 
when time is considered in the calculation. 



In the theory of this science, we suppose all planes to 
be perfectly smooth and even, levers to have no weight, 
cords to be perfectly pliable, apd machines to have no 
friction: in short, all imperfections are to be laid aside, 
until the theory is established, and then proper allow- 
ances are to be made for them. 



article 16. 

OP THE LEVER. 

A bar of Iron, of Wood, or of any other inflexible ma- 
terial, one part of which is supported by a fulcrum or 
prop, and all other parts turn or move on that prop, as 
their centre of motion, is called a lever ; when the lever 
is extended on each side of the prop, these extensions 
are called its arms ; the velocity or motion of every part 
of these arms, is directly as its distance from the centre 
of motion, by the third law of circular motion. 

With respect to the lever, when in equilibrium, — Ob- 
serve the following laws: — 

1. The power and weight are to each other, inverse- 
ly as their distances from the prop, or centre of mo- 
tion. 

That is the power P, fig. 8, Plate I, which is one 
multiplied into its distance B C, from the centre 12, is 
equal to the weight 12 multiplied into its distance A B 
1 ; each product being 12. 



CHAP. II.] MECHANICS. 41 

2. The power is to the weight, as the distance the 
weight moves is to the distance the power moves, re- 
spectively. 

That is, the power multiplied into its distance moved, 
is equal to the weight multiplied into its distance moved. 

3. The power is to the weight, as the perpendicular 
ascent of the weight is to the perpendicular descent of 
the power. 

That is, the power multiplied into its perpendicular 
descent, is equal to the weight multiplied into its perpen- 
dicular ascent. 

4. Their velocities are as their distances from their cen- 
tre of motion, by the 3d law of circular motion, p. 28. 

These simple laws hold universally true, in all me- 
chanical powers or engines ; therefore it is easy (from 
these simple principles) to compute the power of any 
engine, either simple or compound; for it is only to find 
how much swifter the power moves than the weight, or 
how much farther it moves in the same time ; and so 
much is the power (and time of producing it) increased, 
by the help of the engine. 



article 17. 

GENERAL RULES FOR COMPUTING THE POWER OF ANY ENGINE. 

1. Divide either the distance of the power from its 
centre of motion, by the distance of the weight from its 
centre of motion. Or, 

2. Divide the space passed through by the power, by 
the space passed through by the weight, (this space may 
be counted either on the arch, or on the perpendicular 
described by each,) and the quotient will show how much 
the power is increased by the help of the engine ; then 
multiply the power applied to the engine, by that quo- 
tient, and the product will be the power of the engine, 
whether simple or compound. 



42 MECHANICS. [CHAP. II. 

EXAMPLES. 

Let ABC Plate I. fig. 8, represent a lever; then, to 
compute its power, divide the distance of the power P 
from its centre of motion B C 12, by the distance A B 1, 
of the weight W, and the quotient is 12: the power is 
increased 12 times by the engine ; which, multiplied by 
the power applied 1, produces 12, the power of the en- 
gine at A, or the weight W, that will balance P, and 
hold the engine in equilibrio. But suppose the arm A 
B to be continued to E, then, to find the power of the 
engine, divide the distance B C 12, by B E 6, and the 
quotient is two; which, multiplied by 1, the power ap- 
plied, produces 2, the power of the engine, or weight W, 
to balance, P. 

Or divide the perpendicular descent C D of the power 
equal to 6, by the perpendicular ascent E F equal 3 ; and 
the quotient 2, multiplied by the power P equal 1, pro- 
duces 2, the power of the engine at E. 

Or divide the velocity of the power P equal 6, by the 
velocity of the weight w equal 3 ; and the quotient 2 
multiplied by the power 1, produces 2, the power of the 
engine at E. If the power P had been applied at 8 then 
it would have required to have been 1| to balance W, or 
w: because 1| times 8 is 12, which is the momentum of 
both weights W and w. If it had been applied at 6, it 
must have been 2; if at 4, it must have been 3 ; and so 
on for any other distance from the prop or centre of mo- 
tion. 



article 18. 

OF THE DIFFERENT KINDS OF LEVERS. 

There are four kinds of Levers. 

1 . The most common kind, where the prop is placed 
between the weight and power, but generally nearest the 
weight, as otherwise, there would be no gain of power. 

2. When the prop is at one end, the power at the other, 
and the weight between them. 



CHAP. II.] MECHANICS. 43 

3. When the prop is at one end, the weight at the 
other, and the power applied between them. 

4. The bended lever, which diners only in form, but 
not in properties, from the others. 

Those of the first and second kind, have the same pro- 
perties and powers, and produce real mechanical advan- 
tage, because they increase the power; but the third kind 
produces a decrease of power, and is only used to increase 
velocity, as in clocks, watches, and mills, where the first 
mover is slow, and the velocity is increased by the gear- 
ing of the wheels. 

The levers which nature employs in the machinery of 
the human frame, are of the third kind ; for when we lift 
a weight by the hand, the muscle that exerts the force 
to raise the weight, is fastened at about one-tenth of the 
distance from the elbow to the hand, and must exert a 
force ten times as great as the weight raised ; therefore, 
he that can lift 56 lbs. with his arm at a right angle at 
the elbow,exerts a force equal to 560 lbs. by the muscles 
of his arm. 



article 19. 

OF COMPOUND LEVERS. 

Several levers may be applied to act one upon another, 
as 2 13 in fig. 9, Plate I, where No. 1 is of the first 
kind, No. 2 of the second, and No. 3 of the third. The 
power of these levers, united to act on the weight W, is 
found by the following rule, which will hold universally 
true in any number of levers united, or wheels (which 
operate on the same principle) acting upon one another. 

RULE. 

1st. Multiply the power P, into the length of all the 
driving levers successively, and note the product. 

2d. Then multiply all the leading levers into one ano- 
ther successively, and note the product. 



44 MECHANICS. [CHAP. II. 

3d. Divide the first product by the last, and the quo- 
tient will be the weight W, that will hold the machine in 
equilibrio. 

This rule is founded on the first law of the lever, Art. 
16, and on this principle; namely: 

Let the weight W, and power P, be such, that when 
suspended on any compound machine, whether of levers 
united, or of wheels and axles, they hold the machine in 
equilibrio: then if the power P be multiplied into the 
radius of all the driving wheels, or lengths of the driving 
levers, and the product noted, and the weight W multi- 
plied in the radius of all the leading wheels, or lengths of 
the leading levers, and the product noted, these products 
will be equal. If we had taken the velocities, or the cir- 
cumferences of the wheels, instead of their radii, they 
would have been equal also. 

On this principle is founded all rules for calculating 
the power and motion of wheels in mills, &c. See Art. 
20. 

EXAMPLES. 

Given the power P equal to 4 on lever 2, at 8 distance 
from the centre of motion. Required, with what force 
lever 1, fastened at 2 from the centre of motion of lever 
2, must act to hold the lever 2 in equilibrio.* 

By the rule 4x8 the length of the long arm is 32, and 
this divided by 2, the length of the short arm, gives 16, 
the force required. 

Then 16 on the long arm, lever 1, at 6 from the centre 
of motion. Required the weight on the short arm, at 2, 
to balance it. 

By the rule, 16x6= 96, which divided by 2, the short 
arm, gives 48, for the weight required. 

Then 48 is on the lever 3, at 2 from the centre. Re- 
quired the weight at 8 to balance it. 

Then 48 x 2 = 96, which divided by 8, the length of 
the long arm, gives 12, the weight required. 

Given, the power P = 4, on one end of the combination 

* In order to abbreviate the work, I shall hereafter use the following Algebraic 
signs, namely : 



CHAP. II.] MECHANICS. 45 

of levers. Required, the weight W. on the other end, to 
hold the whole in equilibrio. 

Then by the rule, 4 x 8 x 6 x 2 = 384 the product of 
the power multiplied into the length of all the driving 
levers, and 2 x 2 x 8 = 32 the product of all the leading 
levers, and 384 -t- 32 = 12 the weight W required. 



ARTICLE 20. 
CALCULATING THE POWER OF WHEEL WORK. 

The same rule holds good in calculating the power of 
machines consisting of wheels, whether simple or com- 
pound, by counting the radii of the wheels as the levers ; 
and because the diameters and circumferences of circles 
are proportional, we may take the circumferences instead 
of the radii, and it will be the same result. Then, again, 
because the number of cogs in the Wheels constitute the 
circle, we may take the number of cogs and rounds in- 
stead of the circle or radii, and the result will still be the 
same. 

Let fig. 11, Plate IT, represent a water mill (for grind- 
ing grain) double geared. 

Number 8 The water-wheel, 

4 The great cog-wheel, 

2 The wallower, 

3 The counter cog-wheel, 

1 The trundle, 

2 The mill-stones, 

And let the above numbers also represent the radius of 
each wheel in feet. 

Now suppose there be a power of 500 lbs. on the water- 
wheel required, what will be the force exerted on the 
mill-stone, 2 feet from the centre. 

The sign + plus, or more, for addition. 

— minus, or less, for subtraction. 
X multiplied, for multiplication. 
-4- divided, for division. 
= equal, for equality. 
Then, instead of 8 more 4 equal 12, 1 shall write S -f 4 == 19. Instead of 12 less 
4 equal 8, 12 — 4 = 8. Instead of 6 multiplied by 4 equal 2 4, 6 X 4 = 24. And 
instead of 24 divided by 3 equal 8, 24 -~ 3 = 8. 



46 MECHANICS. [CHAP. II. 

Then by the rule, 500 x 8 x 2 x 1 = 8000, and 4x3 
x 2 = 24, by which divide 8000, and it quotes 333,33 lbs. 
the power or force required, exerted on the mill-stone two 
feet from its centre which is the mean circle of a 6 feet 
stone. — And as the velocities are as the distance from the 
centre of motion, by the third law of circular motion, Art. 
13, therefore, to find the velocity of the mean circle of the 
stone 2, apply the following rule; namely: 

1st. Multiply the velocity of the water-wheel into the 
radii or circumferences of all the driving wheels, succes- 
sively, and note the product. 

2. Multiply the radii or circumferences of all the 
leading wheels, successively, and note the product; di- 
vide the first by the last product, and the quotient will 
be the answer. , 

But observe here, that the driving wheels in this rule, 
are the leading levers on the last rule. 

EXAMPLES. 

Suppose the velocity of the water-wheel to be 12 feet 
per second; then by the rule 12x4x3x2 = 288 and 
8 x 2 x 1 = 16, by which divide the first product 288, 
and*this gives 18 feet per second, the velocity of the stone 
2 feet from its centre. 



ARTICLE 21. 

POWER DECREASES AS MOTION INCREASES. 

It may be proper to observe here, that as the velocity 
of the stone is increased, the power to move it is de- 
creased, and as its velocity is decreased, the power on it 
to move it is increased, by the second general law of me- 
chanical powers. This holds universally true in all en- 
gines that can possibly be contrived; which is evident 
from the first law of the lever when in equilibrium, 
namely, the power multiplied into its velocity or dis- 
tance moved, is equal to the weight multiplied into its 
velocity or distance moved. 



CHAP. II.] MECHANICS. 47 

Hence the general rule to compute the power of any 
engine, .simple or compound, Art. 17. If you have the 
moving power, and its velocity or distance moved, given, 
and the velocity or distance of the weight, then, to find 
the weight, (which, in mills, is the force to move the 
stone, &c.) divide that product by the velocity of the 
weight or mill-stone, &c. and this gives the weight or 
force exerted on the stone to move it. But a certain 
quantity or proportion of this force is lost from friction 
in order to obtain a velocity to the stone; which is shown 
in Art. 31. 



ARTICLE 22. 
NO POWER GAINED BY ENLARGING OVERSHOT WATER-WHEELS. 

This seems a proper time to show the absurdity of the 
idea of increasing the power of the mill, by enlarging the 
diameter of the water-wheel, on the principle of lengthen- 
ing the lever; or by double gearing mills where single 
gears will do; because the power can either be increased 
or diminished by the help of engines, while the velocity 
of the body moved is to remain the same. 

EXAMPLE. 

Suppose we enlarge the diameter of the water-wheel 
from 8 to 16 feet radius, fig. 11, Plate II. and leave the 
other wheels unaltered; then, to find the velocity of the 
stone, allowing the velocity of the periphery of the water- 
wheel to be the same (12 feet per second;) by the rule 
12x4x3x2 = 288, and 16 x 2 x 1 = 32, by which 
divide 288, which gives 9 feet in a second, for the velocity 

' O 'ml 

of the stone. 

Then, to find the power by the rule for that purpose, 
Art. 20, 500 x 16 x 2 x 1 = 16,000, and 4 x 3 x 2 = 
24, by which divide 16,000, it gives 666,66 lbs, the 
power. But as velocity as well as power, is necessary in 



48 MECHANICS. [CHAP. II. 

mills, we shall be obliged, in order to restore the velocity, 
to enlarge the great cog-wheel from 4 to 8 radius. 

Then to find the velocity, 12x8x3x2 = 576, and 
16 x 2 x 1 = 32, by which divide 576, it gives 18, the 
velocity as before. 

Then to find the power by the rule, Art. 20, it will be 
333,33 as before. 

Therefore no power can be gained, upon the princi- 
ple of lengthening the lever, by enlarging the water- 
wheel. 

The true advantages that large wheels have over small 
ones, arise from the width of the buckets bearing but a 
small proportion to the radius of the wheel ; because if 
the radius of the wheel be 8 feet, and the width of the 
bucket or float board but 1 fopt, the float takes up 1-8 of 
the arm, and the water may be said to act fairly upon 
the end of the arm, and to advantage. But if the radius 
of the wheel be but 2 feet, and the width of the float 1 
foot, part of the water will act on the middle of the arm, 
and of course, to disadvantage, as the float takes up half 
the arm. The large wheel also serves the purpose of a 
fly-wheel (Art. 30;) it likewise keeps a more regular mo- 
tion, and casts off back water better. (See Art. 70.) 

But the expense of these large wheels is to be taken 
into consideration, and then the builder will find that 
there is a maximum size, (see Art. 44,) or a size that will 
yield him the greatest profit. 



article 23. 

NO POWER GAINED, BUT SOME LOST, BY DOUBLE GEARING MILLS. 

I might go on to show that no power or advantage is 
to be gained by double gearing mills, upon any other 
principles than the following; namely: 

1. When the motion necessary for the stone cannot be 
obtained without having the trundle too small, we are 
obliged to have the pitch of the cogs and rounds, and the 
size of the spindle, large enough to bear the stress of the 



CHAP. II.] MECHANICS. 49 

power; and this pitch of gear, and size of spindle, may- 
bear too great a proportion to the radius of the trundle, 
(as does the size of the float to the radius of the water- 
wheel, Art. 22,) and may work hard. There, therefore, 
may be a loss of power on that account, greater than that 
resulting from friction in double gearing. 

2. By double gearing, the mill may be made more con- 
venient for two pair of stones to one water-wheel. 

Many and great have been the losses sustained by mill- 
builders on account of their not properly understanding 
these principles. I have often met with water wheels of 
large diameter, where those of half the size and expense 
would answer better; and double gears, where single 
would be preferable. 



article 24. 

OF THE PULLEY. 

2. The pulley is a mechanical power well known. 
One pulley, if it be moveable with the weight, doubles 
the power, because each rope sustains half the weight. 

If two or more pulleys be joined together in the com- 
mon way, then the easiest mode of computing their power 
is, to count the number of ropes that join to the lower or 
moveable block, and so many times is the power increased; 
because all these ropes have to be shortened, and all run 
into one rope (called the fall) to which the moving power 
is applied. If there be 4 ropes, the power is increased 
fourfold. See Plate I. fig. 10. 

The objection to this engine is, that there is great loss 
of power, by the friction of the pulleys^ and in the bend- 
ing of the ropes, 



article 25. 

OF THE WHEEL AND AXLE, 



3. The wheel and axle, fig. 17, is a mechanical power, 
similar to the lever of the first kind; therefore, whejs 

4 



50 MECHANICS. [CHAP. II. 

the power is to the weight, as the diameter of the axle is 
to the diameter of the wheel ; or when the power multi- 
plied into the radius of the wheel is equal to the weight 
multiplied into the radius of the axle, this engine is in 
equilibrium. 

The loss of power is but small in this instrument, be- 
cause it has but little friction. 



article 26. 

OF THE INCLINED PLANE. 

4. The inclined plane is the fourth mechanical power; 
and in this the power is to the, weight, as the perpendicu- 
lar height of the plane is to its length. This is of use in 
rolling heavy bodies, such as barrels, hogsheads, &c.,into 
wheel carriages, &c, and for letting them down again. 
See Plate I. fig. 5. If the height of the plane be half its 
length, then half the force will roll the body up the plane, 
that it would lift it perpendicularly to the same height, 
but it has to travel double the distance. 



ARTICLE 27. 
OF THE WEDGE. 

5. The wedge is only an inclined plane. Whence, in 
the common form of it, the power applied will be to the 
resistance to be overcome, as the thickness of the wedge 
is to the length thereof. This is a very useful mechani- 
cal power, and, for some purposes, excels all the rest; 
because with it we can effect what we cannot with any 
other in the same time; and its power, I think, may be 
computed in the following manner. 

If the wedge be 12 inches long and 2 inches thick, 
then the power to hold it in equilibrio is as 1 to balance 
12 resistance; that is 12 resistance pressing on each side 
of the wedge and when struck with a mallet the whole 
force of the weight of the mallet, added to the whole 



CHAP. II.] MECHANICS. 51 

force of the power exerted in the stroke, is communicated 
to the wedge in the time it continues to move: and this 
force to produce effect, is as the square of the velocity 
with which the mallet strikes, multiplied into its weight ; 
therefore, the mallet should not be too large, because it 
may be too heavy for the workman's strength, and will 
meet too much resistance from the air, so that it will lose 
more by lessening the velocity, than it will gain by its 
weight. Suppose a mallet of 10 lbs. strike with 5 velocity, 
its effective momentum is 250; but if it strike with 10 
velocity, then its effective momentum is 1000. The 
effect produced by the strokes will be as 250 to 1000 ; 
and all the force of each stroke, except what may be de- 
stroyed by the friction of the wedge, is added in the wedge, 
until the sum of these forces amounts to more than the 
resistance of the body to be split, which therefore must 
give way; but when the wedge does not move, the whole 
force is destroyed by the friction ; therefore the less the 
inclination of the sides of the wedge, the greater the re- 
sistance we can overcome by it, because it will be easier 
moved by the stroke. 



ARTICLE 28. 
OF THE SCREW. 

6. The screw is the last mentioned mechanical power, 
and may be denominated a circular inclined plane, (as 
will appear by wrapping a paper, cut in form of an in- 
clined plane, round a cylinder.) It is used in combina- 
tion with a lever of the first kind, (the lever being ap- 
plied to force the weight upon the inclined plane:) this 
compound instrument is a mechanical power, of exten- 
sive use, both for pressure, and raising great weights. 
The power applied is to the weight it will raise, as the 
distance through which the weight moves, is to the dis- 
tance through which the power moves; that is, as the dis- 
tance of two contiguous threads of the screw is to the cir- 
cle the power describes, so is the power to the weight it 
will raise. If the distance of the thread be half an inch, 



52 MECHANICS. [CHAP. II. 

and the lever be fifteen inches radius : and the power ap- 
plied be 10 lbs. then the power will describe a circle of 
94 inches, while the weight rises half an inch ; then as 
half an inch is to 94 inches, so is 10 lbs. to 1880 lbs. the 
weight the engine would raise with 10 lbs. power. But 
this is supposing the screw to have no friction, of which 
it has a great deal. 



article 29. 



OF THE FLY-WHEEL AND ITS USE. 



Before I dismiss the subject of mechanical powers, I 
shall take some notice of the fly-wheel, the use of which 
is to regulate the motion of engines, it is best made of 
cast iron, and should be of a circular form, that it may 
not meet with much resistance from the air. 

Many have supposed this wheel to be an increaser of 
power, whereas it is, in reality, a considerable destroyer 
of it: which appears evident, when we consider that it 
has no motion of its own, but receives all its motion from 
the first mover ; and as the friction of the gudgeons, and 
the resistance of the air are to be overcome, this cannot 
be done without the loss of some power ; yet this wheel 
is of great use in many cases ; namely : 

1st. For regulating the power, where it is irregularly 
applied, such as the treadle and crank moved by the foot 
or hand ; as in spinning-wheels, turning-lathes, flax-mills, 
or where steam is applied, by a crank, to produce a cir- 
cular motion. 

2. Where the resistance is irregular, or by jerks, as 
in saw-mills, forges, slitting-mills, powder mills, &c, the 
fly-wheel by its inertia, regulates the motion ; because 
if it be very heavy, it will require a great many little 
shocks or impulses of power to give it a considerable 
velocity ; and it will, of course, require as many equal 
shocks to resist or destroy the velocity it has acquired. 

While a rolling or slitting-mill is running empty, the 



CHAP. II.] MECHANICS. 53 

force of the water is employed in generating momentum 
in the fly-wheel ; which force accumulated in the fly, will 
be sufficient to continue the motion without much abate- 
ment, while the sheet of metal is running between the 
rollers ; whereas, had the force of the water been lost 
while the mill was empty, its motion might be destroyed 
before the metal passed through the rollers. Where wa- 
ter is scarce, its effect maybe so far aided by a fly-wheel, 
as to overcome a resistance to which the direct force of 
the water is unequal, that is, where the power is required 
at intervals only. 

A heavy water-wheel frequently produces all the effect 
of a fly-wheel, in addition to its direct office. 



article 30. 

ON FRICTION. 

We have hitherto considered the action and effect of 
the mechanical powers, as they would answer to the 
strictness of mathematical theory, were there no such 
thing as friction, or rubbing of parts upon each other j but 
it is generally allowed, that one-fourth of the effect of a 
machine is, at a medium, destroyed by it : it will be pro- 
per to treat of it next in course. 

From what I can gather from different authors, and by 
my own experiments, it appears that the doctrine of fric- 
tion is as follows, and we may say it is subject to the fol- 
lowing laws; namely; 

Laws of Friction. 

1. Friction is greatly influenced by the smoothness or 
roughness, hardness or softness, of the surface rubbing 
against each other. 

2. It is in proportion to the pressure, or load, that is, a 
double pressure will produce a double amount of friction, 
a triple pressure a triple amount of friction, and so of any 
other proportionate increase of the load. 

3. The friction does not depend upon the extent of 
surface, the weight of the body remaining the same. 



54 MECHANICS. [CHAP. II. 

Thus, if a parellelopiped, say of four inches in width and 
one in thickness, as F, plate II. fig. 13, be made smooth, 
and laid upon a smooth plane A. B. C. D. and the weight 
P. hung over a pulley, it will require the weight P. to 
draw the body F along, to be equal, whether it be laid on 
its side or on its edge. 

The experiments of Vince led him to conclude that the 
law, as thus laid down, was not correct ; but, those more 
recently performed justify the conclusion, that it is so, 
the deviations being so trifling, as not to affect the gene- 
ral result. 

4. The friction is greater after the bodies have been 
allowed to remain for some time at rest, in contact with 
each other, than when they are first so placed ; as, for 
example, a wheel turning upon gudgeons will require a 
greater weight to start it after remaining for some hours 
at rest, than it would at first. 

The cause of this appears to be, that the minute aspe- 
rities which exist even upon the smoothest bodies, gradu- 
ally sink into the opposite spaces, and thus hold upon 
each other. 

It is for the same reason, that a greater force is re- 
quired to set a body in motion, than to keep it in motion. 
If about J the amount of a weight be required to move 
that weight along in the first instance, | will suffice to 
keep it in motion. 

5. The friction of axles does not at all depend upon 
their velocity ; thus a rail-road car travelling at the rate 
of twenty miles an hour, will not have been retarded by 
friction, more than another which travels only ten miles 
in that time. 

It appears, therefore, from the last three laws, that the 
amount of friction is as the pressure directly, without re- 
gard to surface, time or velocity. 

6. Friction is greatly diminished by unguents, and this 
diminution is as the nature of the unguents, without re- 
ference to the substances moving over them. The kind 
of unguent which ought to be employed depends prin- 
cipally upon the load; it ought to suffice just to prevent 
the bodies from coming into contact with each other. 
The lighter the weight, therefore, the finer and more 
fluid should be the unguent, and vice versa. 



CHAP. II.] MECHANICS. 55 



ARTICLE 31. 
ON THE FRICTION OF DIFFERENT SUBSTANCES. 

It is well known that in general the friction of two dis- 
similar substances is less than that of similar substances, 
although alike in hardness. The most recent experi- 
ments upon this subject are those of Mr. Rennie, of Eng- 
land, performed in the year 1825, and published in the 
Philosophical Transactions. Many of the experiments 
were performed upon substances which do not concern 
the present work ; those with the metals, and other hard 
substances, were tried both with and without unguents. 

The following facts were deduced from those in which 
unguents were not employed : 

Table showing the amount of friction (without unguents) of different 
substances, the insistent weight being 36 lbs., and within the limits 
of abrasion of the softer substances. 

Parts of the 
whole weights. 
Brass on wrought iron ._.--- 7.38 

Brass on cast iron - - - - - - -7.11 

Brass on steel - 7.20 

Soft steel on soft steel 6.85 

Cast iron on steel ....... 6.62 

Wrought iron on wrought iron .... - 6.26 

Cast iron on cast iron ------- 6.12 

Hard brass on cast iron - - - - - - 6.00 

Cast iron on wrought iron ------ 5.87 

Brass on brass - - - - - -.- - 5.70 

Tin on cast iron - - - - - - - - 5.59 

Tin on wrought iron ------- 5.53 

Soft steel on wrought iron ------ 5.28 

With unguents it was found that, with gun metal on 
cast iron, with oil intervening, the insistent weight be- 
ing 10 cwt.the friction amounted to T |j of the pressure ; 
that by a diminution of weight, the friction was rapidly 
diminished. 

That cast iron on cast iron, under similar circum- 
stances, showed less friction; and that this was still far- 
ther diminished by hog's lard. 



56 MECHANICS. [CHAP. II. 

That yellow brass, on cast iron, with anti-attrition com- 
position of black lead and hog's lard, increased friction 
with light weights, and greatly diminished it with heavy 
weights, showing extremely irregular results. 

That yellow brass, on cast iron, with tallow, gave the 
least friction, and may therefore be considered the best 
substance under the circumstances tried. 

That yellow brass, on cast iron, with soft soap, gave 
the second best result, being superior to oil. 



ARTICLE 32. 
OF MECHANICAL CONTRIVANCES, TO REDUCE FRICTION. 

Friction is considered as of two kinds, the first is oc- 
casioned by the rubbing of the surfaces of bodies against 
each other, the second by the rolling of a circular body, 
as that of a carriage wheel upon the ground, or rollers 
placed under a heavy load. In the preceding articles 
the first kind of friction has been considered ; it is that 
which we most frequently have to encounter, and which 
produces the greatest expenditure of power. When the 
parts can be made to roll over each other, the resistance 
is greatly diminished. To change one into the other has 
been the object of those mechanical contrivances denomi- 
nated friction wheels, and friction rollers. 

A, in plate II. fig. 14, may represent the gudgeon of a 
wheel set to run upon the peripheries of two wheels C, C, 
which pass each other ; these are called friction wheels. 
This gudgeon, instead of grinding, or rubbing its sur- 
face, or the surface on which it presses, carries that sur- 
face with it, causing the wheels C, C, to revolve. A 
gudgeon, B, is sometimes set upon a single wheel, with 
supporters to keep it on, which produces an analogous 
effect. 

Less advantage, however, has been derived from fric- 
tion wheels in heavy machinery, than had been antici- 
pated ; and it has been found, in many cases, that they do 
not compensate for the expense of construction, and their 



CHAP. II.] MECHANICS. 57 

liability to get out of order. The rubbing friction still 
exists in their gudgeons, and it has frequently happened 
that instead of turning them, the gudgeon resting upon 
them has rolled round, whilst they have remained at 
rest. 

The principle of the roller has already been noticed, 
and its mode of action is shown in fig. 15, plate II., where 
A B may represent a body of a 100 tons weight, with the 
under side perfectly smooth and even, set on rollers per- 
fectly hard and smooth, rolling on a horizontal plane, C D, 
perfectly hard, smooth, and horizontal. If these rollers 
stand precisely parallel to each other, the least imagina- 
ble force would move the load; even a spider's web would 
be sufficient, were time allowed to overcome the inertia. 

These suppositions, however, can never be realized, 
and although in this mode of action there will be the 
least possible rubbing friction, there will be enough to 
produce considerable resistance. 

It has been attempted to apply this principle to wheel 
carriages, to the sheaves of blocks on ship board, and to 
the axles of other machinery, by an ingenious con- 
trivance called Garnett's friction rollers, for which a 
patent was obtained in England about fifty years ago, 
by an American gentleman from New Jersey. This 
contrivance is shown at fig. 16, Plate II. The outside 
ring B, C, D, may represent the box of a carriage wheel, 
the inside circle A the axle ; the circles a a a a a a the 
rollers round the axle, and between it and the box ; the 
inner ring is a thin plate for the pivots of the rollers to run 
in, to keep them at a proper distance from each other. 
When the wheel turns, the rollers pass round on the 
axle, and on the inside of the box, and that almost with- 
out friction, because there is no rubbing of the parts in 
passing one another. 

Such friction rollers, from the use of which so much 
was expected, have not been found to answer in practice. 
If not made with the most perfect accuracy, they gather 
as they roll, and thus increase the friction. In carriages, 
and indeed in every kind of machines, subject to an ir- 
regular jolting motion, the rollers, and the cylinder with- 



58 MECHANICS. [CHAP. II. 

in which they revolve, soon become indented, and are 
then worse than useless. 



ARTICLE 33. 

OF MAXIMUMS, OR THE GREATEST EFFECTS OF ANY MACHINE. 

The effect of a machine is the distance to which it 
moves a body of given weight, in a given time; or, in 
other words, the resistance which it overcomes. The 
weight of the body multiplied into its velocity, is the 
measure of this effect. 

The theory published by philosophers, and received 
and taught as true, for several centuries past, is, that 
any machine will work with its greatest perfection when 
it is charged with just 4-9ths of the power that would 
hold it in equilibrio, and then its velocity will be just J 
of the greatest velocity of the moving power. 

To explain this, we may suppose the water-wheel 
Plate II, fig. 17, to be of the undershot kind, 16 feet di- 
ameter, turned by water issuing from under a 4 feet head, 
with a gate drawn 1 foot wide, and 1 foot high, then the 
force will be 250 lbs., because that is the weight of the 
column of water above the gate, and its velocity will be 
16,2 feet per second, as shall be shown under- the head 
of Hydraulics ; the wheel will then be moved by a pow- 
er of 250 lbs., and if let run empty, will move with a ve- 
locity of 16 feet per second ; but if the weight W be hung 
by a rope to the axle of two feet diameter, and we 
continue to add to it until it stops the wheel, and holds 
it in equilibrio, the weight will be found to be 2000 lbs. 
by the rule, Art. 19; and then the effect of the machine 
is nothing, because the velocity is nothing: but as we 
decrease the weight W, the wheel begins to move, and 
its velocity increases accordingly ; and then the product 
of the weight multiplied into its velocity, will increase 
until the weight is decreased to 4-9ths of 2000 = 888,7, 
which multiplied into its velocity or distance moved, 
will produce the greatest effect, and the velocity of the 



CHAP. II.] MECHANICS. 59 

wheel will then be J of 16 feet, or 5,33 feet per second. 
So say those who have treated of it. 

This will probably appear plainer to a beginner, if he 
conceives this wheel to be applied to work an elevator, 
as E, Plate II, fig. 17, to hoist wheat, and suppose that 
the buckets, when all full, contain nine pecks, and will 
hold the wheel in equilibrio, it is evident it will then 
hoist none, because it has no motion; and in order to ob- 
tain motion, we must lessen the quantity in the buckets, 
when the wheel will begin to move, and hoist faster and 
faster until the quantity is decreased to 4-9ths or 4 pecks, 
and then, by the theory, the velocity of the machine will 
be J of the greatest velocity, when it will hoist the great- 
est quantity possible in a given time: for if we lessen the 
quantity in the buckets below 4 pecks, the quantity hoist- 
ed in any given time will be lessened; this is the esta- 
blished theory. 



article 34. 

OLD THEORY INVESTIGATED. 

In order to investigate this theory, and the better to 
understand what has been said, let us consider as follows; 
namely: 

1. That the velocity of spouting water, under 4 feet 
head, is 16 per second, nearly. 

2. The section or area of the gate drawn, in feet, 
multiplied by the height of the head in feet, gives the 
cubic feet in the whole column, which multiplied by 
62,5 (the weight of a cubic foot of water) gives the 
weight or force of the whole column pressing on the 
wheel. 

3. That the radius of the wheel, multiplied by the 
force, and that product divided by the radius of the 
axle, gives the weight that will hold the wheel in equi- 
librio. 

4. That the absolute velocity of the wheel, subtracted 
from the absolute velocity of the water, leaves the re- 



60 MECHANICS. [CHAP. II. 

lative velocity with which the water strikes the wheel 
when in motion. 

5. That as the radius of the wheel, is to the radius of 
the axle, so is the velocity of the wheel, to the velocity 
of the weight hoisted on the axle. 

6. That the effects of spouting fluids, are as the 
squares of their velocities (see Art. 45, law 6,) but the 
instant force of striking fluids is as their velocities 
simply. See Art. 8. 

7. That the weight hoisted, multiplied into its per- 
pendicular ascent gives the effect. 

8. That the weight of water expended, multiplied 
into its perpendicular descent, gives the power used per 
second. 

On these principles I have calculated the following 
scale: first, supposing the force of striking fluids to be as 
the square of their striking or relative velocity, which 
brings out the maximum agreeably to the old theory, 
namely: 

When the load at equilibrio is 2000, then the maxi- 
mum load is 888,7 = 4-9ths of 2000, the effect being then 
greatest, namely, 591,98, as appears in the sixth column; 
and v .then the velocity of the wheel is 5,333 feet per se- 
cond, equal to J of 16, the velocity of the water, as ap- 
pears in the fifth line of the scale: but there is an evident 
error in the first principle of this theory, by counting 
the instant force of the water on the wheel to-be as the 
square of its striking velocity, it cannot, therefore, be 
true. See Art. 41. 

I then calculate upon this principle, namely: that if 
the instant force of striking fluids is as their velocity 
simply, then the load that the machine will carry, with 
its different velocities, will also be as the velocity simply, 
as appears in the 7th column; and the load, at a maxi- 
mum, as 1000 lbs. = | of 2000, the load at equilibrio, 
when the velocity of the wheel is 8 feet = § of 16, the 
velocity of the water per second; and then the effect is 
at its greatest, as shown in the 8th column, namely, 
1000, as appears in the 4th line of the scale. 

This I call the new theory, (because I found that 



CHAP. II.] MECHANICS. 61 

William Waring had also, about the same time, esta- 
blished it, see Art. 37,) namely, that when any machine 
is charged with just one-half of the load that will hold it 
in equilibrio, its velocity will be just one-half of the na- 
tural velocity of the moving power, and then its effect 
will be at a maximum, or the greatest possible. 

It thus appears that a great error has been long over- 
looked by philosophers, and that this has rendered the 
theory of no use in practice, but led many into expen- 
sive failures. 



62 



MECHANICS. 



[CHAP. II, 



§ 






t3 






s 

£ 



5* 



*2 



Ratio of the power and ef- 
fect at a maximum, the 
power being 4000 in each 
case. 




Maximum 
by new 
theory 

4 to 1 

10 to 1.47 

Maximum 
by old 
theory. 


Effect by the new theory. 


CD 


©r-©t-cooo>o 

o « c n i^ io n t- 

t» O) o o> OO QO f C<5 


Weight hoisted, according to 
the new theory. 


05 


OOOOCQIOCOOI 
I-. H 1— 1 r-i — _l OJ 


Effect by the old theory. 




00 

lO Ol C5 SO IO t— 

r i © <-o ~ © oj im 

OOOWOCDCimOOO 

h n ifl ui in o >o M 


Weight hoisted, according to 
the old theory. 


r£J 


ic >— ' © — oo lc lc — i o 
nooooooo^Ciroo 

OhO|10C-(BO-0 

— — a 


Velocity of the weight as- 
cending. 




SO Lffl 

its io so c>> to 
inw t- so so in ;;■) © 

MrirtH 


Velocity with which the wa- 
ter strikes the wheel in 
motion, or relative velo- 
city. 


CD 


so 
so 

SO 

o^tooood-Ti^a 


Velocity of the wheel per 
second, by supposition. 


SO 


CO 
00 
00 

S£>CJOaosoioi.o^FCT© 


feet. 
Radius of the wheel .... 8 
Radius of the axle .... 1 

Section of the gate in square feet > 1 

Height of the head of water . • 4 
Velocity of the water per second . 16 
Weight of the column of water J lbs. 

pressing on the wheel f 250 
The weight that holds the wheel > 2qqq 

in equilibrio 5 



CHAP. II.] MECHANICS. 63 

ARTICLE 35. 



NEW THEORY DOUBTED. 



Although I know that the velocity of the wheel, by 
this new theory, is, (though rather slow,) much nearer to 
general practice than by the old, yet I am led to doubt its 
correctness, for the following reasons ; namely : 

There are 16 cubic feet of water, equal to 1000 lbs. 
expended in a second ; which, multiplied by its perpen- 
dicular descent, 4 feet, produces the power 4000. The 
ratio of the power and effect by the old theory, is as 10 
to 1,47, and by the new, as 4 to l,as appears in the 9th 
column of the scale ; this is a proof that the old theory is 
incorrect, and sufficient to make us suspect that there is 
some error in the new. And as the subject is of the 
greatest consequence in practical mechanics, I therefore 
have endeavoured to discover a true theory, and will show 
my work, in order that if I establish a theory, it may be 
the easier understood, if right, or detected, if wrong. 



article 36. 

ATTEMPT TO DEDUCE A TRUE THEORY. 

I constructed the apparatus fig. 18, Plate II., which re- 
presents a simple wheel with a rope passing over it, and 
the weight P, 100 lbs. at one end to act by its gravity, 
as a power to produce effects, by hoisting the weight w 
at the other end. 

This seems to be on the principles of the lever, and 
overshot wheel ; but with this exception, that the quan- 
tity of descending matter, acting as power, will still be 
the same, although the velocity will be accelerated, 
whereas, in overshot wheels, the power on the wheel is 
inversely, as the velocity of the wheel. 

Here we must consider, 

1. That the perpendicular descent of the body P, per 
second, multiplied into its weight, shows the power. 

2. That the weight w, when multiplied into its per- 
pendicular ascent, gives the effect. 

3. That the natural velocity of the falling body P, is 16 



64 



MECHANICS. 



[CHAP. II. 



feet the first second, and the distance it has to fall 16 
feet. 

4. That we suppose the weight w, or resistance, will 
occup}^ its proportional part of the velocity, that is, if w 
be = | P, the velocity with which P will then descend, 
will be | 16 = 8 feet per second. 

5. If w be = P, there can be no velocity, consequently 
no effect; and if w = o, then P will descend 16 feet in a 
second, but produce no effect, because the power, although 
1600 per second, is applied to hoist nothing. 

Upon these principles I have calculated the following 
scale. 



A SCALE 

FOR DETERMINING THE 

Maximum, Charge and Velocity of 100 lbs. 

DESCENDING BY ITS GRAVITY. 



o 
re 

P 

2 


3 

p 

c 

»-* 

p 

11 


3 

CD 
cr 

B* 


M 

i% 

CD O 

CD JS 
2. ° 
CO* B 

f 8, 


Proportion of t 
which is th 
and weight. 


M 

re 5 

►CJ CD 
P--3 

.-■ B" 

5S" 

O B J 


o 

P re 
re /T* 

c 

2; 5" 


p 

o" 
o 




5° 


3^ 

P b 


CD 

5?" 




re tJ- 

«! » 
re <: 


go cc 

p ^ 

GO c- 


&. co' 
re 

en .-»■ 


B* 

CD 

o 




o 
b 

re 

re 

-re 


""" re 5 

nl % 

CD CD 


GO O 

&- 
CD 


CD o 

CfQ*2. 


O o 
rt-" ° 

^re 


2 ro 

re 

r+ ^ 

t-j re 
re ox; 

** B^ 


2 !=" 
re re 

B 
re si 


3 

re 

i-i 

P 
B 




CD <-. 

^ CO 

• CD 
O 
O 

B 


CD 

CO 

P 

CD 


i*8 

b-£ 

™ CD 

re P- 


o ■*. 

o g. 

I 5 ' 

re a 


CO e-* 

CD 

° Si 
B 

c 


TO t-S 

CD 

8^ 

3 

P-3 


re 
o 






O 


5' 


P-o- 




r+ 






lbs. 
100 


feet. 
16 


lbs. 


feet. 


feet. 





1600 


10:0 






1 


.16 


15.84 


15.84 


15S4 


10:0 






10 


1.6 


14.4 


144 


1440 


10:1 








20 


3.2 


12.8 


256 


1280 


10:2 








30 


4,8 


11.2 


336 


1120 


10:3 








40 


6.4 


9.6 


384 


960 


10:4 


Maximum, 






50 
60 


8. 
9.6 


8. 
6.4 


400 

384 


800 
640 


10:5 
10:6 


by new theo- 
ry- 






70 


11.9 


4.8 


336 


480 


10:7 






80 


12.8 


3.2 


256 


320 


10:8 








90 


14.4 


1.6 


144 


160 


10:9 








99 


15.84 


.16 


15.8 


16 


10:99 




100 


16. 


0. 


0. 










CHAP. II.] MECHANICS. 65 

By this scale it appears, that when the weight w is 
= 50 = f P the power, the effect is at a maximum, name- 
ly, 400, as appears in the 6th column, when the velocity 
is half the natural velocity, namely, 8 feet per second ; and 
then the ratio of the power to the effect is as 10 to 5, as 
appears in the 8th line. 

By this scale it appears, that all engines that are moved 
by one constant power, which is equally accelerated in 
its velocity, must be charged with weight or resistance 
equal to half the moving power, in order to produce 
the greatest effect in a given time ; but if time be not re- 
garded, then the greater the charge, so as to leave any 
velocity, the greater the effect, as appears by the 8th 
column. So that it appears that an overshot wheel, if 
it be made immensely capacious, and to move very slow- 
ly, majr produce effects in the ratio of 9,9 to 10 of the 
power. 



ARTICLE 37. 
SCALE OF EXPERIMENTS. 

The following is a scale of actual experiments made 
to prove w r hether the resistance occupies its proportion 
of the velocity, in order that I might judge whether the 
foregoing scale was founded on true principles : the ex- 
periments were not very accurately performed, but were 
often repeated, and the results were always nearly the 
same. See Plate II. %. IS. 



66 



MECHANICS. 



[CHAP. II. 



A SCALE 



EXPERIMENTS. 



40 



CD ^ 

CD 

S±P 



5 3 



W S> I-. 



o <* 

3 »-(o 

E&£ 

PT a CD 
§"* 

•S-FdS" 

&•" 3 

CD << o 

p §-5 

B iO 1 



5!" o 

|S 

O O 



7 
6 
5 
4 

3.5 

3 

o 

i 





S T3 
P. 03 



20 

15.5 

12 

10 

9 

6.5 
6 
5 





2X6 
2.6x5 
3.33x4 

4 X '3.5 

4.44x3 

6x2 
86.6x1 



cT^ 



a^ 



•a ^ 






pa b 



P 



o 

12 
13 
13.32 

14 

13.32 
12 

6.6 





14 

18.2 

23.31 

28 

31.08 
42 
46.2 
56 



^«5 



S: 



£5' 

r+ CD 

t5-ffl 

2. » 



$ < 



10:8 

10:7.1 

10:5.1 

10:5 

10:4.2 

10:2 

10:1 



24 

33.8 

44.35 

maximum 
new theory. 

59.14 

72 maximum 

33.56 



CHAP. II.] MECHANICS. 67 

By this scale it appears, that when the power P falls 
freely without any load, it descends 40 feet in five equal 
parts of time; but when charged with 3,5 lbs. = P, 
which was 7 lbs., it then takes up 10 of those parts of 
time to descend the same distance ; which seems to show, 
that the charge occupies its proportional part of the 
whole velocity, which was wanted to be known, and the 
maximum appears as in the last scale. It also shows that 
the effect is not as the weight multiplied into the square 
of its ascending velocity, this being the measure of the 
effect that would be produced by the stroke on a non- 
elastic body. 

Atwood, in his Treatise on Motion, gives a set of ac- 
curate experiments, to prove (beyond doubt) that the 
conclusion I have drawn is right; namely: — That the 
charge occupies its proportional part of the whole velo- 
city. 

These experiments partly confirmed me in what I have 
called the New Theory; but still doubting, and after I 
had formed the foregoing tables, I called, for his assist- 
ance, on the late ingenious and worthy friend, William 
Waring, teacher in the Friends' Academy, Philadel- 
phia, who informed me that he had discovered the error 
in the old theory, and corrected it in a paper which he 
had laid before the Philosophical Society of Philadelphia, 
wherein he had shown that the velocity of the undershot 
water-wheel, to produce a maximum effect, must he just 
one half the velocity of the water. 



article 38. 

WILLIAM WARINg's THEORY. 

The following are extracts from the above mentioned 
paper, published in the third volume of the transactions 
of the American Philosophical Society, held at Philadel- 
phia, p. 144. 

After his learned and modest introduction, in which 
he shows the necessity of correcting so great an error as 



68 MECHANICS. [CHAP. II. 

the old theory, he begins with these words; namely: — 
" But, to come to the point, I would just premise these 



DEFINITIONS. 

If a stream of water impinge against a wheel in mo- 
tion, there are three different velocities to be considered 
appertaining thereto; namely: 

1st. The absolute velocity of the water. 

2d. The absolute velocity of the wheel. 

3d. The relative velocity of the water to that of the 
wheel; that is, the difference of the absolute velocities, 
or the velocity with which the water overtakes or strikes 
the wheel. 

Now the mistake consists in supposing the momentum 
or force of the water against the wheel, to be in the du- 
p'icate ratio of the relative velocity; whereas: 

Prop. i. 

The force of an invariable stream impinging against a 
mill-wheel in motion, is in the simple proportion of the 
relative velocity, 

For, if the relative velocity of a fluid against a single 
plane be varied either by the motion of the plane or of 
the fluid from a given aperture, or both, then the num- 
ber of particles acting on the plane, in a given'time, and 
likewise the momentum of each particle being respec- 
tively as the relative velocity, the force, on both these 
accounts, must be in the duplicate ratio of the relative 
velocity, agreeably to the common theory, with respect 
to the single plane ; but the number of these planes, or 
parts of the wheel acted on in a given time, will be as 
the velocity of the wheel, or inversely as the relative ve- 
locity; therefore, the moving force of the wheel must be 
as the simple ratio of the relative velocity. Q. U. D. 

Or, the proposition is manifest from this consideration, 
that while the stream is invariable, whatever be the ve- 
locity of the wheel, the same number of particles, or 
quantity of fluid, must strike it somewhere or other in a 
given time; consequently, the variation of the force is 



CHAP. II.] MECHANICS. 69 

only on account of the varied impingent velocit} r of the 
same body, occasioned by a change of motion in the 
wheel ; that is, the momentum is as the relative velocity. 

Now this true principle, substituted for the erroneous 
one in use, will bring the theory to agree remarkably 
with the notable experiments of the ingenious Smeaton, 
published in the Philosophical Transactions of the Royal 
Society of London, for the year 1751, vol. 51 ; for which 
the honorary annual medal was adjudged by the society, 
and presented to the author by their president. 

An instance or two of the importance of this correction 
may be adduced, as follows: 

Prop. ii. 

The velocity of a wheel, moved by the impact of a 
stream, must be half the velocity of the fluid, to produce 
the greatest effect possible. 

( V = the velocity, M = the momentum, of the fluid. 
I v = the velocity, P = the power, of the wheel. 
Then V — v = their relative velocity by definition 3d. 



And as V : V— v : : M : m x V— v = P, (Prop. 1,) which 

V 

xv=:P,vx M x V — v 3 == a maximum ; hence Vv — v a = 
V 

a maximum, and its fluxion (v being a variable quantity) 
= Vv — 2vv = O ; therefore = \ V; that is, the velocity of 
the wheel = half that of the fluid, at the place of impact 
when the effect is a maximum. Q. E. D. 

The usual theory gives v = J V, where the error is not 
less than one-sixth of the true velocity. 

Wm. Waring." 
Philadelphia, llh 
9th mo. 1790. 



Hh ) 



70 MECHANICS. [CHAP. II. 

I here omit quoting Proposition III. as it is altogether 
algebraical, and refers to a figure; I am not writing for 
men of science, but for practical mechanics. 



article 39. 

Extract from a further paper, read in the Philosophical So- 
ciety, April 5th, 1 793 . 

" Since the Philosophical Society were pleased to fa- 
vour my crude observations on the theory of mills with 
a publication in their transactions, I am apprehensive 
some part thereof may be misapplied; it being therein 
demonstrated, that 'the force of an invariable stream im- 
pinging against a mill-wheel in motion, is in the simple 
direct ratio of the relative velocity.' Some may suppose 
that the effect produced should be in the same proportion, 
and either fall into an error, or finding by experiment, 
the effect to be as the square of the velocity, conclude the 
new theory to be not well founded ; I therefore wish 
there had been a little added, to prevent such misapplica- 
tion, v 'before the Society had been troubled with the read- 
ing of my paper on that subject, perhaps something like 
the following. 

The maximum effect of an undershot wheel, produced 
by a given quantity of water, in a given time; is in the 
duplicate ratio of the velocity of the water ; for the effect 
must be as the impetus acting on the wheel, multiplied 
into the velocity thereof: but this impetus is demon- 
strated to be simply as the relative velocity, Proposition 
I., and the velocity of the wheel, producing a maximum, 
being half of the water, by Proposition II., is likewise as 
the velocity of the water ; hence the power acting on the 
wheel multiplied into the velocity of the wheel, or the 
effect produced, must be in the duplicate ratio of the ve- 
locity of the water. Q. E. D. 

Corollary. Hence the effect of a given quantity of 
water, in a given time, will be as the height of the head, 
because this height is as the square of the velocity. This 
also agrees with experiment. 



CHAP. II.] MECHANICS. 71 

If the force, acting on the wheel, were in duplicate 
ratio of the water's velocity, as is usually asserted, then 
the effect would be as the cube thereof, when the quan- 
tity of water and time are given, which is contrary to the 
result of experiment." 



article 40. 



WARING S THEORY DOUBTED. 



From the time I first called on William Waring, until 
I read his publication on the subject (after his death,) I 
had rested partly satisfied with the new theory, as I 
have called it, with respect to the velocity of the wheel, 
at least, but finding that he had not determined the 
charge, as well as the velocity, by which we might have 
compared the ratio of the power and the effect produced, 
and that he had assigned somewhat different reasons for 
the error, and having found the motion to be rather too 
slow to agree with practice, I began to suspect the whole, 
and resumed the search for a true theory; thinking that 
perhaps no person had ever yet considered every thing 
that effects the calculation; I therefore premised the fol- 
lowing 

POSTULATES. 

1. A given quantity of perfectly elastic, or solid mat- 
ter, impinging on a fixed obstacle, its effective force is 
as the squares of its different velocities, although its in- 
stant force may be as its velocities simply, because the 
distance it will recede after the stroke through any re- 
sisting medium, will be as the squares of its impinging 
velocities. 

2. An equal quantity of elastic matter, impinging on a 
fixed obstacle with a double velocity, produces a quad- 
ruple effect, their effects are as the squares of their velo- 
cities. Consequently — 

3. A double quantity of said matter, impinging with a 



72 MECHANICS. [CHAP. II. 

double velocity, produces an octuple effect, or their ef- 
fects are as the cubes of their velocities, Art. 47 and 67. 

4. If the impinging matter be non-elastic, such as 
fluids, then the instant force will be but half, but the ra- 
tio will be the same in each case. 

5. A double velocity, through a given aperture, gives 
a double quantity to strike the obstacle or wheel; there- 
fore the effects will be as the cubes of the velocity. See 
Art. 47. 

6. But a double relative velocity cannot increase the 
quantity that is to act on the wheel; therefore, the ef- 
fect can only be as the square of the velocity, by postu- 
late 2. 

7. Although the instant force and effects of fluids 
striking on fixed obstacles, are only as their simple velo- 
cities, yet their effects, on moving wheels, are as the 
squares of their velocities; because, 1st, a double striking 
velocity gives a double instant force, which bears a dou- 
ble load on the wheel ; and 2d, a double velocity moves 
the load a double distance in an equal time, and a double 
load moves a double distance, is a quadruple effect. 



article 41. 

SEARCH FOR A TRUE THEORY, COMMENCED ON A NEW PLAN. 

It appears that we have applied wrong principles in our 
search after the true theory of the maximum velocity, and 
load of undershot water-wheels, or other engines moved by 
a constant power, that does not increase or decrease in 
quantity on the engine, as on an overshot water-wheel, as 
the velocity varies. 

Let us suppose water to issue from under ahead of 16 
feet, on an undershot water-wheel; then, if the wheel move 
freely with the water, its velocity will be 32,4 feet per se- 
cond, but will bear no load. 

Again; suppose we load it, so as to make its motion 
equal only to the velocity of water spouting from under 
a head of 15 feet; it appears evident that the load will 



CHAP. II.] 



MECHANICS. 



then be just equal to the 1 foot of the head, the velocity 
of which is checked ; and this load multiplied into the 
velocity of the wheel ; namely : 31,34 x 1=31,34, for the 
effect. 

This appears to be the true principle, from which we 
must seek the maximum velocity and load, for such en- 
gines as are moved by one constant power; and on this 
principle I have calculated the following scale. 



A SCALE 

FOR DETERMINING THE 

TRUE MAXIMUM VELOCITY AND LOAD 

FOR 

UNDERSHOT WHEELS. 



H 


M 


<! 


r- 1 


H 




o 

p 

3 -1 

re 
P 
P- 


re 
P 

era o- 
o 2 


elocity of 
cond, bein 
the water 
unbalance 


oad of the 
part of th 
of which i 


fleet per se 
of the w 
load. 




3 


o' re 


the whee' 
g equal 
from und 
d. 


oi re . 

3^ O X 


re o 
re 3 




P 
re 


o re 


re S- o 


c re 




P 
o 

o" 


m d 

< 3 

re EL 

re p 

f 3 

o 

re 


1 in feet per s 
the velocity 
er the head li 


• g 2. 

CL 3 
Ci re 

3 £- 
o 


t^crq 

re S' 
j^l. re 

a* 1 re 
^ o 

re 






o 


ore 


a S- 


a-^ 




feet. 


feet. 


feet. 






16 


16 


32.4 












15 


31.34 


1 


31.34 






14 


30.2 


2 


60.4 






12 


28 


4 


112 






10 


25.54 


6 


153.24 






8 


22.8 


8 


182.4 






7 


21.43 


9 


192.87 






6 


19.84 


10 


198.4 






5.66 


19.27 


10.33 


198.95 






5.33 


18.71 


10.66 


199.44 


Maximum motion 




5 


18 


11 


198 


and load. 




4 


16.2 


12 


194.4 






3 


14 


13 


172 






2 


11.4 


14 


159.6 






1 


8.1 


15 


120 












16 








74 MECHANICS. [CHAP, II. 

In this scale let us suppose the aperture of the gate to 
be a square foot; then the greatest load that will balance 
the head will be 16 cubic feet of water, and the different 
loads will be shown in cubic feet of water. 

It appears by this scale, that when the wheel is load- 
ed with 10,66 cubic feet of water, just § of the greatest 
load, its velocity will be 18,71 feet per second, just, 577 
parts of the velocity of the water, and the effect produced 
is then at a maximum, or the greatest possible, namely : 
199,44. 

To make this more plain, let us suppose A B, Plate 
II. fig. 19, to be a fall of water of 16 feet, which we 
wish to apply to produce the greatest effect possible, by 
hoisting water on its side, opposite to the power applied. 
First, on the undershot principle, where the water acts 
by its impulse only. Let us suppose the water to strike 
the wheel at I, then if we let the wheel move freely with- 
out any load, it will move with the velocity of the water, 
namely, 32,4 feet per second, but will produce no effect, 
if the water issue atC; although there be 32,4 cubic feet 
of water expended, under 16 feet perpendicular descent. 
Let the weight of a cubic foot of water be represented by 
unity.or 1, for ease in counting ; then 32,4 x 16 will show 
the power expended, per second, namely, 518,4; and the 
water it hoists multiplied into its perpendicular ascent, or 
height hoisted, will show the effect. Then in order to 
obtain effect from the power, we load the wheel ; the sim- 
plest way of doing which, is, to cause the tube of water C 
D, to act on the back of the bucket at I; then, if C D be 
equal to A B, the wheel will be held in equilibrio; this is 
the greatest load, and the whole of the fall A B is ba- 
lanced, and no part left to give the wheel velocity; there- 
fore the effect = o. But if we make C D = 12 feet of A 
B, then from 4 to A, = 4 feet, is left unbalanced, to give 
velocity to the wheel, which being loaded with 12 feet, 
would be exactly balanced by 12 on the other side, and 
left perfectly free to move either way by the least force 
applied be3^ond this balance. Therefore it is evi- 
dent that the whole pressure or force of 4 feet of A B, 
will act to give velocity to the wheel, and, as there is 



CHAP. II.] MECHANICS. 75 

no resistance to oppose the pressure of these 4 feet, the 
velocity will be that of water spouting from under a 4 
feet head, namely, 16,2 feet per second, which is shown 
by the horizontal line, 4 = 16,2 and the perpendicular 
line, 12 = 12, represents the load of the wheel; the rec- 
tangle or product of these two lines forms a parallelogram, 
the area of which is a true representation of the effect, 
namely, the load 12 multiplied into 16,2, the distance it 
moves per second = 194,4, the effect. In like manner we 
may try the effect of different loads; the less the load, the 
greater will be the velocity. The horizontal lines all 
show the velocity of the wheel, produced by the respec- 
tive heads left unbalanced, and the perpendicular lines 
show the load on the wheel; and we find, that when the 
load is 10,66 = f 16, the load at equilibrio, the velocity of 
the wheel will be 18,71 feet per second, which is T y^ parts, 
or a little less than 6 tenths, or | the velocity of the water, 
and the effect is 199,44, the maximum, or greatest possi- 
ble; and if the aperture of the gate be 1 foot, the quantity 
will be 18,71 cubic feet per second. The power being 
18,71 cubic feet expended per second, multiplied by 16 
feet of the perpendicular descent, produce 299,36, the 
ratio of the power and effect, being as 10 to 6, JL, or 
nearly as 3 : 2; but this is supposing none of the force 
lost by non-elasticity. 

This may appear plainer, if we suppose the water to 
descend in the tube A B, and by its pressure, to raise 
the water in the tube CD; for it is evident, that if we 
raise the water to D, we have no velocity, therefore, 
effect = o. Then again, if we open the gate at C, we 
have 32,4 feet per second velocity; but because we do 
not hoist the water to any height, effect is = o. There- 
fore, the maximum is somewhere between C and D. 
Then suppose we open gates of 1 foot area, at different 
heights, the velocity will show the quantity of cubic 
feet raised; which multiplied by the perpendicular 
height of the gate from C, or height raised, gives the 
effect, and the maximum as before. But here we must 
consider that in both these cases the water acts as a 
perfectly definite quantity, which will produce effects 



76 MECHANICS. [CHAP. II. 

equal to elastic bodies, or equal to its gravity, (See Art. 
59,) which is unattainable in practice: whereas, when it 
acts by percussion only, it communicates only half of its 
original force, on account of its non-elasticity, the other 
half being spent in splashing about; therefore, the true 
effect will be ^^ (a little more than J) of the moving 
power; because nearly J is lost to obtain velocity, and 
half of the remaining § is lost by non-elasticity. These 
are the reasons why the effect produced by an undershot 
wheel is only half that produced by an overshot wheel, 
the perpendicular descent and quantity of water being 
equal. And this agrees with Smeaton's experiments 
(See Art. 68 ;) but if we suppose the velocity of the wheel 
to be one-third that of the water = 10,8, and the load to 
be | of 1 6, the greatest load at'equilibrio, which is = 7,1 1 1 , 
as by old theory, then the effect will be 10,8 x 4,9 of 16 
= 76,79 for the effect which is quite too little, the moving 
power being 32,4 cubic feet of water multiplied by 16 
feet descent = 518,4; the effect by this theory being less 
than -^ of the power, about half equal to the effect, by 
experiment, which effect is set on the outside of the dotted 
circle in fig. 19. The dotted lines join the corner of the 
parallelograms, formed by the lines that represent the 
loads and velocities, in each experiment or supposition, 
the areas of which truly represent the effect, and the 
dotted line A a d x, meeting the perpendicular line x E 
in the point x, forming the parallelogram A B "C x ; truly 
represents the power == 518,4. 

Again, if we suppose the wheel to move with half the 
velocity of the water, namely, 16,2 feet per second ; and 
to be loaded with half the greatest load = 8 according to 
Waring's theory; then the effect will be 16,2 x 8 = 129,6 
for the effect, about T 2 ^- of the power, which is still less 
than by experiment. All this seems to confirm the maxi- 
mum brought out on the new principles. 

But, if we suppose, according to the new principle, 
that when the wheel moves with the velocity of 16,2 
feet per second, which is the velocity of a 4 feet head, 
it will then bear as a load the remaining twelve feet, then 
the effect will be 16,2 x 12 = 194,4 which nearly agrees 



CHAP. II.] MECHANICS. 77 

with practice: but as most mills in practice move faster, 
and few slower, than what I call the true maximum, this 
shows it to be nearest the truth; the true maximum ve- 
locity being ,577 of the velocity of the water, and the mills 
in practice moving with f, and generally quicker.* 

This scale also establishes a true maximum charge for 
an overshot wheel; that is, if we suppose the power, 
or quantity of water on the wheel at once, to be always 
the same, even although the velocity vary, which would 
be the case, if the buckets were kept always full; for, 
suppose the water to be shot into the wheel at a, and 
by its gravity to raise the whole water again on the op- 
posite side; then as soon as the water rises in the wheel 
to d, it is evident that the wheel will stop, and the effect 
bb = o ; therefore, we must let the water out of the 
wheel, before it rises to d, which will be, in effect, to lose 
part of the power to obtain velocity. If the buckets, both 
descending and ascending, carrv a column of water 1 
foot square, then the velocity of the wheel will show the 
quantity hoisted as before, which multiplied by the per- 
pendicular ascent, shows the effect; and the quantity 
expended multiplied by the perpendicular descent, shows 
the power ; and we find, that when the wheel is loaded 
with § of the power, the effect will be at a maximum ; 
that is, the whole of the water is hoisted, f of its whole 

* The reason why the wheel hears so great a load at a maximum, appears to he 
as follows; namely: — 

A 16 feet head of water over a gate of 1 foot, issues 32,4 cubic feet of water in 
a second, to strike the wheel in the same time, that a heavy body will take up in 
falling through the height of the head. Now, if 16 cubic feet of elastic matter 
were to fall 16 feet, and strike an elastic plane, it would rise hy the force of the 
stroke to the height from whence it fell; or, in other words, it will have force suf- 
ficient to hear a load of 16 cubic feet. 

Again, if 32 cubic feet of non-elastic matter, moving with the same velocity 
(with which the 16 feet of elastic matter struck the plane,) strike a wheel in the 
same time, although it communicate only half the force that gave it motion; yet 
because there is a double quantity striking in the same time, the effects will he 
equal; that is, it will bear a load of 16 cubic feet, or the whole column, to hold it 
in equilibrio. 

Again, to check the whole velocity, requires the whole column that produces 
the velocity; consequently, to check any part of the velocity, will require such a 
part of the column, as is equal to the part checked; and we find by Art. 41, that, 
to check the velocity of the wheel, so as to be ,577 of the velocity of the water, 
it requires 2-3ds of the whole column, and this is the maximum load. When the 
velocity of the wheel is multiplied by 2-3ds of the column, it produces the effect, 
which will be to the power, as 3S to 100; or, as S,« to 10, somewhat mor3 than 
l-3d, and the friction and resistance of the air may reduce it to l-3d. 



78 MECHANICS. [CHAP. II. 

descent ; or § of the water, the whole of the descent ; 
therefore, the ratio of the power to the effect is as 3 to 2, 
or double the effect of an undershot wheel : but this is 
supposing the quantity in the buckets to be always the 
same, whereas, in overshot wheels, the quantity in the 
buckets is inversely as the velocity of the wheel; that is, 
the slower the motion of the wheel, the greater the quan- 
tity in the buckets, and the greater the velocity, the less 
the quantity ; but again, as we are obliged to let the over- 
shot wheel move with a considerable velocity, in order to 
obtain a steady, regular motion to the mill, we shall find 
this charge to be always nearly right; hence, I deduce 
the following theory. 



article 42. 
THEORY. 

A TRUE THEORY DEDUCED. 

'This scale seems to have shown, 

1. That when an undershot mill moves with ,577 or 
nearly ,6 of the velocity of the water, it will then bear a 
charge equal to § of the load that will hold the wheel in 
equilibrio, and then the effect will be at a maximum. The 
ratio of the power to the effect will be as 3 to 1, nearly. 

2. That when an overshot wheel is charged with | of 
the weight of the water acting upon the wheel, then the 
effect will be at a maximum ; that is, the greatest effect 
that can be produced by said power in a given time, and 
the ratio of the power to the effect will be as 3 to 2, 
nearly. 

3. That | of the power is necessarily lost, to obtain ve- 
locity, or to overcome the inertia of the matter ; and this 
will hold true with all machinery that requires velocity 
as well as power. This I believe to be the true theory 
of water-mills, for the following reasons ; namely ; 

1. The theory is deduced from original reasoning, with- 
out depending much on calculation. 



CHAP. II.] MECHANICS. . 79 

2. It agrees better than any other theory with the in- 
genious Smeaton's experiments. 

3. It agrees best with real practice, according to the 
best of my information. 

Yet I do not wish any person to receive it implicitly, 
without first informing himself whether it be well founded, 
and in accordance with actual experience ; for this reason 
I have quoted the experiments of Smeaton at full length, 
in this work, that the reader may compare them with the 
theory. 

TRUE THEOREM FOR FINDING THE MAXIMUM CHARGE FOR UNDER- 
SHOT WHEELS. 

As the square of the velocity of the water, or wheel 
empty, is to the height of the head, or pressure, which 
produced that velocity, so is the square of the velocity of 
the wheel loaded, to the head, pressure, or force, which 
will produce that velocity ; and this pressure, deducted 
from the whole pressure or force, will leave the load 
moved by the wheel, on its periphery or verge, which 
load multiplied by the velocity of the wheel, shows the 
effect. 

PROBLEM. 

Let V = 32,4, the velocity of the water or wheel, 
P = 16, the pressure, force, or load, at equilibrio, 
v = the velocity of the wheel, supposed to be 16,2 

feet, per second, 
p = the pressure, force, or head, to produce said 

velocity, 
1 == the load on the wheel, 
Then to find 1, the load, we must first find p ; 
Then, by 

Theorem VV : P : : vv : p. 
And P— p = 1 
VVp = vvP 

vvl 
P = — = 4 

VV 
1 = P— p = 12, the load. 



80 MECHANICS. [CHAP. II. 

Which, in words at length, is the square of the velocity 
of the wheel multiplied by the whole force, pressure or 
head of the water, and divided by the square of the 
velocity of the water, quotes the pressure, force, or head 
of water, that is left unbalanced by the load to produce 
the velocity of the wheel ; which pressure, force, or head, 
subtracted from the whole pressure, force, or head, leaves 
the load that is on the wheel. 



article 43. 

Theorem j "or finding the velocity of the wheel, when we have 
the velocity of the water, load at equilibrio, and load on the 
toheel given. 

As the square root of the whole pressure, force or load 
at equilibrio, is to the velocity of the water, so is the 
square root of the difference, between the load on the 
wheel, and the load at equilibrio, to the velocity of the 
wheel. 

PROBLEM. 

Let V = velocity of the water = 32,4, 

P = pressure, force, head or load at equilibrio = 
16, 1= the load on the wheel, suppose 12, 
v = velocity of the wheel, 
Then by the 

Theorem V P : V : : v ¥^\ : v 
And vP X v = Vv/P^l : v 
* V V P— 1 
V= =16,2 

vP 

That is, in words at length, the velocity of the water 
32,4 multiplied by the square root of the difference, be- 
tween the load on the wheel, 12, and the load at equili- 
brio 16 = 2 = 64,8 divided by the square root of the load 
at equilibrio, quotes 16,2, the velocity of the wheel. 

Now, if we seek for the maximum, by either of these 
theorems, it will be found as in the scale, fig. 19. 



The velocity of 
the wheel. 



CHAP. II.] MECHANICS. 81 

Perhaps here may now appear the true cause of the 
error in the old theory, Art. 34, by supposing the load 
on the wheel to be as the square of the relative velocity 
of the water and wheel. 

And of the error in what I have called the new theo- 
ry, by supposing the load to be in the simple ratio of 
the relative or striking velocity of the water, Art. 38; 
whereas it is to be found by neither of these proportions. 

Neither the old nor the new theory agrees with prac- 
tice; therefore we may suspect they are both founded in 
error. 

But if what I call the true theory should be found to 
accord with experience, the practitioner need not be 
much concerned on what it is founded. 



article 44. 

Of the Maximum Velocity for Overshot Wheels, or those 
that are moved by the weight of the Water. 

Before I dismiss the subject of maximums, I think it 
best to consider, whether this doctrine will apply to the 
motion of the overshot w T heel. It seems to be the gene- 
ral opinion of those who consider the matter, that it will 
not ; but that the slower the wheel moves, provided it be 
capacious enough to hold all the water, without losing 
any until it be delivered at the bottom of the wheel, the 
greater will be the effect, which appears to be the case 
in theory (see Art. 36,) but how far this theory "will hold 
good in practice is to be considered. Having met with 
the ingenious James Smeaton's experiments, where he 
shows that when the circumference of his little wheel, 
of 24 inches diameter, (head 6 inches) moved with about 
3,1 feet per second (although the greatest effect was di- 
minished about 2^ of the whole) he obtained the best ef- 
fect with a steady, regular motion. Hence he concludes 
about three feet to be the best velocity for the circum- 
ference of overshot mills. See Art. 68. I undertook to 
compare this theory of his with the best mills in practice, 
6 



82 MECHANICS. [CHAP. II. 

and finding that those of about 17 feet diameter general- 
ly moved about 9 feet per second, being treble the velo- 
city assigned by Smeaton, I began to doubt the theory, 
which led me to inquire into the principle that moves an 
overshot wheel; and this I found to be that of a body de- 
scending by its gravity, and subject to all the laws of fall- 
ing bodies (Art. 10,) or of bodies descending inclined 
planes, and curved surfaces (Art. 11;) the motion being 
equably accelerated in the whole of its descent, its velocity 
being as the square root of the distance descended through; 
and, that the diameter of the wheel was the distance 
through which the water descended. From thence I 
concluded, that the velocity of the circumference of 
overshot wheels was as the square root of their diame- 
ters, and of the distance the' water has to descend, if it 
be a breast or a pitch-back wheel : then, taking Smea- 
ton's experiments, with his wheel of two feet diameter, 
for a foundation, I say, as the square root of the diame- 
ter of Smeaton's wheel is to its maximum velocity, so 
is the square root of the diameter of any other wheel, to 
its maximum velocity. Upon these principles I have 
calculated the following table, and having compared it 
with at least 50 mills in practice, found it to agree so 
nearly with all those best constructed, that I have reason 
to believe it is founded on true principles. 

If an overshot wheel move freely, without resistance, 
it will require a mean velocity between that- of the wa- 
ter coming on the wheel, and the greatest velocity it 
would acquire, by falling freely through its whole de- 
scent : therefore, this mean velocity will be greater than 
the velocity of the water coming on the wheel ; conse- 
quently, the backs of the buckets will overtake the wa- 
ter, and drive a great part of it out of the wheel. But, 
the velocity of the water being accelerated by its gra- 
vity, overtakes the wheel, perhaps half way down, and 
presses on the buckets, until it leaves the w 7 heel : there- 
fore the water presses harder upon the buckets in the 
lower than in the upper quarter of the wheel. Hence 
appears the reason why some wheels cast their water; 
which is always the case, when the head is not sufficient 



CHAP. II.] MECHANICS. 83 

to give it velocity enough to enter the buckets. But 
this depends also much on the position of the buckets, 
and the direction of the shute into them. It, however, 
appears evident, that the head of water above the wheel, 
should be nicely adjusted to suit the velocity of the 
wheel. Here we may consider, that the head above the 
wheel acts by percussion, or on the same principles with 
the undershot wheel; and, as we have shown, (Art. 40) 
that the undershot wheel should move with nearly 2-3ds 
of the velocity of the water, it appears, that we should 
allow a head over the wheel, that will give such velocity 
to the water, as will be to that of the wheel, as 3 to 2„ 
Thus, the whole descent of the water of a mill-seat, 
should be nicely divided between head and fall, to suit 
each other, in order to obtain the best effect, and a 
steady-moving mill. First, find the velocity with which 
the wheel will move, by the weight of the water, for any 
diameter you may suppose you will take for the wheel, 
and divide said velocity into two parts ; then try if your 
head be such as will cause the water to come on with a 
velocity of 3 such parts, making due allowances for the 
friction of the water, according to the aperture, See Art. 
55. Then, if the buckets and the direction of the shute 
be right, the wheel will receive the water well, and move 
to the best advantage, keeping a steady, regular motion 
when at work, loaded or charged with a resistance equal 
to 2-3ds of its power. (Art. 41, 42.) 



84 



MECHANICS. 



[chap. II. 



A TABLE 



VELOCITIES OF THE CIRCUMFERENCE 

OF 

OVERSHOT WHEELS 

Suitable to their Diameters, or rather to the Fall, after the Water strikes the 
Wheel; and of the head of Water above the Wheel, suitable to said Velocities; 
also of the Number of Revolutions the Wheel will perform in a Minute, when 
rightly charged. 



w 


< 


a 


> 




3 


S" 
3 

cd 


o o 


^ O CD 


r? r+ Q- 

^ ct p; 


H 
o 


3 


to 


"It rf 


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CHAP. II.] MECHANICS. 85 

This doctrine of maximums is very interesting, and is 
to be met with, in many occurrences through life. 

1. It has been shown, that there is a maximum load 
and velocity for all engines, to suit the power and velo- 
city of the moving power. 

2. There is also a maximum size, velocity and feed 
for mill-stones, to suit the power; a maximum velocity 
for rolling screens, and bolting-reels, by which the great- 
est work can be done in the best manner, in a given 
time. 

3. A maximum degree of perfection and closeness, 
with which grain is to be manufactured into flour, so as 
to yield the greatest profit by the mill in a day or week, 
and this maximum is continually changing with the 
prices in the market, so that what would be the greatest 
profit at one time, will sink money at another. See 
Art. 113. 

4. A maximum weight for mallets, axes, sledges, &c, 
according to the strength of those that use them. 

A true attention to the principles of maximums, will 
prevent us from running into many errors. 



86 HYDRAULICS. [CHAP. III. 



CHAPTER III. 
HYDRAULICS. 

PRELIMINARY REMARKS. 

The science which treats upon the mechanical pro- 
perties and effects of water and other fluids, has most 
commonly been divided into two branches, Hydrosta- 
tics and Hydraulics. Hydrostatics treats of the weight, 
pressure, and equilibrium of fluids, when in a state of 
rest. Hydraulics treats of water in motion, and the 
means of raising, conducting and using it for moving 
machinery, or for other purposes. These two divisions 
are so intimately connected with each other, that the 
latter could not be at all understood without an acquaint- 
ance with the former; and it is not necessary, in a work 
like'the present, to treat of them separately. Considered 
abstractedly, the same laws obtain in the pressure and 
motion of water, as those which belong to solid bodies, 
and in the last chapter, on Mechanics, this similarity has 
led to some notice of the effects produced by water, 
which, strictly speaking, would belong to the present. 
In doing this, utility has been preferred to a strict adhe- 
rence to svstem. 

In treating of the elementary principles of Hydrau- 
lics, it is necessary to proceed upon theoretical prin- 
ciples : but let it always be recollected that from various 
causes resulting from the constitution of fluids, and par- 
ticularly from that essential property in them, the per- 
fect mobility of their particles among each other, the 
phenomena actually exhibited in nature or in the pro- 
cesses of art, in which the motion of water is concerned, 
deviate so very considerably from the deductions of the- 
ory, that the latter must be considered as a very imper- 
fect guide to the practical mill-wright and engineer. It 



CHAT. III.] HYDRAULICS. 87 

is not to be inferred from this circumstance, that such 
theoretical investigations are false and useless ; they are 
still approximations, which serve as guides to a certain 
extent. Their defectiveness arises from our inability to 
form an estimate of the many disturbing causes which 
influence the motion of fluids; whilst in the mechanics of 
solids we have, in many cases, no other correction to 
make in our theoretical deductions, than to allow for the 
effect of friction. 

" The only really useful method of treating a branch 
of knowledge so circumstanced, is to accompany a very 
concise account of such general principles as are least 
inapplicable to practice, by proportionately copious de- 
tails of the most accurate experiments which have been 
instituted, with a view to ascertain the actual circum- 
stances of the various phenomena." {Lardnerh Hydro- 
statics.) Such has been the course pursued, to a conside- 
rable extent, by the author of this work, and in pursu- 
ing this subject, under the present head of Hydraulics, 
we shall consider only such parts of the science as im- 
mediately relate to our purpose, namely, such as may 
lead to the better understanding of the principles and 
powers of water, acting on mill-wheels, and conveying 
water to them. 



article 45. 

OF SPOUTING FLUIDS. 

Spouting fluids observe the following laws: 

1. Their velocities and powers, under equal pressures, 
or equal perpendicular heights, and equal apertures, are 
equal in all cases.* 

2. Their velocities, under different pressures or per- 
pendicular heights, are as the square roots of those pres- 

* It makes no difference whether the water stands perpendicularly, or inclined 
above the aperture, [see Plate III. fig. 22,] provided the perpendicular height be 
the same; or whether the quantity be great or small, provided it be sufficient to 
keep the fluid up to the same height. 



88 HYDRAULICS. [CHAP. II. 

sures, or heights, and their perpendicular heights, or 
pressures, are as the squares of their velocities.* 

3. Their quantities expended through equal apertures, 
in equal times, under unequal pressures, are as their ve- 
locities simply .t 

4. Their pressures or heights being the same, their 
effects are as their quantities expended.^ 

5. Their quantities expended being the same, their 
effects are as their pressure, or height of their head di- 
rectly. § 

6. Their instant forces with equal apertures, are as 
the squares of their velocities, or as the height of their 
heads directly. 

7. Their effects are as their quantities, multiplied into 
the squares of their velocities. || See Art. 46. 

8. Therefore, their effects or powers with equal aper- 
tures, are as the cubes of their velocities.1T 

* This law is similar to the 4th law of falling bodies, their velocities being as 
the square root of their spaces passed through; and by experiment it is known, 
that water will spout from under a four feet head, with a velocity of 16,2 feet per 
second, and from under a 16 feet head, 32,4 feet per second, which is only double 
to that of a 4 feet head, although there be a quadruple pressure. Therefore, by 
this law, we can find the velocity of water spouting from under any given head: 
for as the square root of 4 equal 2, is to 16,2 its velocity, so is the square root of 
16 equal 4, to 32,4 squared, to 16, its head: by which ratio we can find the head 
that will produce any velocity. 

1 It is evident, that a double velocity will vent a double quantity. 

t If the pressure be equal, the velocity must be equal; and it is evident, that 
double quantity, with equal velocity, will produce a double effect. 

§ That is, if we suppose 16 cubic feet of water to issue from under a 4 feet head 
in a second, and an equal quantity to issue in the same time from under a 16 feet 
head, then their effects will be as 4 to 16. But we must note, that the aperture 
in the last case, must be only half of that in the first, as the velocity will be double. 

|| This is evident from this consideration; namely: that a quadruple impulse is 
required to produce a double velocity, by law 2d, where the velocities are as the 
square roots of their heads : therefore their effects must be as the squares of their 
velocities. 

U The effects of striking fluids with equal apertures are as the cubes of their 
velocities, for the following reasons, namely: 1st. If an equal quantity strike 
with double velocity, the effect is quadruple on that account by the 7th law; and 
a double velocity expends a double quantity by 3d law; therefore, the effect is 
augmented to the cube of the velocity. — The theory for undershot wheels agrees 
with this law also. 



CHAP. III.] 



HYDRAULICS. 



89 



9. Their velocity, under any head, is equal to the ve- 
locity that a heavy body would acquire in falling from 
the same height.* 

10. Their velocity is such, under any head or height, 
as will pass over a distance equal to twice the height of 
the head, in a horizontal direction, in the time that a 
heavy body falls the distance of the height of the head. 

11. Their action and reaction are equal.t 

12. They being non-elastic, communicate only half 
their real force by impulse, in striking obstacles; but ky 
their gravity produce effects equal to elastic or solid 
bodies.^ 

A SCALE. 

Founded on the 3d, 6th, and 7th laws, showing the effects of striking Fluids with 
different Velocities. 



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* The falling body is acted on by the whole force of its own gravity, in the 
whole of its descent through any space; and the whole sum of this action that is 
acquired as it arrives at the lowest point of its fall is equal to the pressure of the 
whole head or perpendicular height above the issue; therefore their velocities are 
equal. 

t That is, a fluid reacts back against the penstock with the same force that it 
issues against the obstacle it strikes ; this is the principle by which Barker's mill , 
and all those that are denominated improvements thereon, move. 

t When non-elastic bodies strike an obstacle, one- half of their force is spent in 
a lateral direction, in changing their figure or in splashing about. See Art. 9. 

For want of due consideration or knowledge of this principle, many have been 
the errors committed by applying water to act by impulse, when it would have 
produced a double effect by its gravity. 



90 HYDRAULICS. [cHAP. III. 

ARTICLE 46. 

DEMONSTRATION OF THE 7tH LAW OF SPOUTING FLUIDS. 

Let A F. (plate III. fig. 26,) represent a head of water 16 feet high, 
and suppose it divided into 4 different heads of 4 feet each, as BCD 
E ; then suppose we draw a gate of 1 foot square at each head succes- 
sively, always sinking the water in the head, so that it will be but 4 
feet above the centre of the gate in each case. 

Now it is known that the velocity under a 4 feet head, is 16,2 feet 
p» second; to avoid fractions say 16 feet, which will issue 16 cubic 
feet of water per second ; and for sake of round numbers, let unity or 
1 represent the quantity of a cubic foot of water ; then, by the 7th law 
the effect will be as the quantity multiplied by the square of the ve- 
locity; that is, 16 multiplied by 16 is equal to 256, which multiplied 
by 16, the quantity, is equal to 4096, the effect of each 4 feet head, 
and 4096 multiplied by 4 is equal to 16384, for the sum of effects of 
all the 4 feet heads. 

Then, as the velocity under a 16 feet head is 32,4 feet, to avoid frac- 
tions say 32, the gate must be drawn to only half the size, to vent the 
16 cubic feet of water per second as before ( because the velocity is 
double :) then to find the effect, 32 multiplied by 32 is equal to 1024; 
which, multiplied by 16, the quantity, gives the effect 16384, equal the 
sum of ali the 4 feet heads, which agrees with the practice and ex- 
perience of the best teachers. But if their effects were as their veloci- 
ties simply, then the effect of each 4 feet head would be, 16 multiplied 
by 16, equal to 256; which multiplied by 4, is equal to 1024, for the 
sum of the effects of all the 4 feet heads ; and 16 multiplied by 32 equal 
to 512, for the effect of the 16 feet head, which is only half of the ef- 
fect of the same head when divided into 4 parts; which is contrary to 
both experiment and reason. 

Again, let us suppose the body A of quantity 16, to -be perfectly 
elastic, to fall 16 feet and strike F, a perfectly elastic plane, it will 
(by laws of falling bodies) strike with a velocity of 32 feet per second, 
and rise 16 feet to A again. 

But if it fall only to B, 4 feet, it will strike with a velocity of 16 feet 
per second, and rise 4 feet to A again. Here the effect of the 16 feet 
fall is 4 times the effect of the 4 feet fall, because the body rises 4 times 
the height. 

But if we count the effective momentum of their strokes to be as 
their velocities simply, then 16 multiplied by 32 is equal to 512, the 
momentum of the 16 feet fall; and 16 multiplied by 16 is equal to 256 ; 
which, multiplied by 4, is equal to 1024, for the sum of the momentums 
of the strokes of 16 feet divided into 4 equal falls; which is absurd. 
But if we count their momentums to be as the squares of their velocities, 
the effects will be equal. 

Again, it is evident that whatever impulse or force is required to 
give a body velocity, the same force or resistance will be required to 
stop it; therefore, if the impulse be as the square of the velocity pro- 
duced, the force or resistance will be as the squares of the velocity 



CHAP. III.] HYDRAULICS. 91 

also. But the impulse is as the squares of the velocity produced, which 
is evident from this consideration: Suppose we place a light body at 
the gate B, of 4 feet head, and pressed with 4 feet of water; when the 
gate is drawn it will fly off with the velocity of 16 feet per second ; 
and if we increase the head to 16 feet it will fly off with 32 feet per 
second. Then, as the square of 16 equal to 256 is to the square of 32 
equal to 1024, so is 4 to 16. Q,. E. D. 



ARTICLE 47. 

THE 7TH LAW IS IN ACCORDANCE WITH PRACTICE. 

Let us compare this 7th law with the theory of undershot mills, es- 
tablished Art. 41, where it is shown that the power is to the effect as 
3 to 1. By the 7th law, the quantity shown by the scale, Plate II., to 
be 32,4 multiplied by 1049,76, the square of the velocity, which is 
equal to 3401,2124, the effect of the 16 feet head; then, for the effect 
of a 4 feet head, with equal apertures, quantity by scale 16,2, multi- 
plied by 262,44, the velocity squared, is equal to 425,1528; the effect 
of a 4 feet head ; here the ratio of the effect is as 8 to 1. 

Then, by the theory, which shows that an undershot wheel will raise 
l-3d of the water that turns it, to the whole height from which it de- 
scended, the l-3d of 32,4 the quantity, being equal to 80,8, multiplied 
by 16, perpendicular ascent, which is equal to 172,8 effect of a 16 ket 
head: and l-3d of 16,2 quantity, which is equal to 5,4 multiplied by 
4, perpendicular ascent is equal to 21,6 effect of a 4 feet head, by the 
theory; and here again the ratio of the effects is as 8 to 1 ; and, 
as 3401,2124, the effect of 16 feet head, ~) , . , 
is to 425,1825, the effect of a 4 feet head, 5 Dy 7Ul law ' 
so is 172,8, the effect of 6 feet head, ? l tl f1 
to 21,6, the effect of 4 feet head, $ Dy tne meoi T- 

The quantities being equal, their effects are as the height of their 
heads directly, as by 5th law, and as the squares of their velocities, as 
by the 7th law. Hence it appears, that the theory agrees with the 
established laws. 

Application of the Laws of Motion to Undershot Wheels. 

To give a short and comprehensive detail of the ideas 
I have collected from different authors, and from the re- 
sult of my own reasoning on the laws of motion and of 
spouting fluids, as they apply to move undershot mills, I 
refer to fig. 44, Plate V. 

Let us suppose two large wheels, one of 12 feet, and 



92 HYDRAULICS. [CHAP. III. 

the other of 24 feet radius, the circumference of the 
largest will then be double that of the smallest : and let A 
16, and C 16, be two penstocks of water, of 16 feet head 
each, then, — 

1. If we open a gate of 1 square foot at 4, to admit 
water from the penstock A 16, to impinge on the small 
wheel at I, the water being pressed by 4 feet head, will 
move 16 feet per second (we omit fractions.) The instant 
pressure or force on that gate being four cubic feet of 
water, it will require a resistance of 4 cubic feet of wa- 
ter from the head C 16 to stop it, and hold it in equili- 
brio, (but we suppose the water cannot escape, unless the 
wheel moves, so that no force be lost by non-elasticity.) 
Here equal quantities of matter, with equal velocities, 
have their momentums equal. 

2. Again, suppose we open a gate of 1 square foot at 
A 16 under 16 feet head, it will strike the large wheel 
at k, with velocity 32, its instant force or pressure being 
16 cubic feet of water; it will require 16 cubic feet re- 
sistance, from the head C 16, to stop or balance it. In 
this case, the pressure, or instant force, is quadruple to 
the first, and so is the resistance, but the velocity only 
double. In these two cases the forces and resistances 
being equal quantities, with equal velocities, their mo- 
mentums are equal. 

3. Again, suppose the head C 16 to be raised to E, 
16 feet above 4, and a gate drawn l-4th of a square foot, 
then the instant pressure on the float I of the small wheel, 
will be 4 cubic feet, pressing on 1-4 th of a square foot, 
and will exactly balance 4 cubic feet, pressing on 1 
square foot from the head A 16 ; and the wheel will bo 
in equilibrio, (supposing the water cannot escape until 
the wheel moves as before,) although the one has power 
of velocity 32, and the other only 16, feet per second ; 
their loads at equilibrio are equal, consequently, their 
loads at a maximum velocity and charge will be equal, 
but their velocities different. 

Then, to try their effects, suppose, first, the wheel to 
move by the 4 feet head, its maximum velocity to be 
half the velocity of the water, which is 16, and its max- 
imum load to be half its greatest load, which is 4, by 
Waring's theory ; then the velocity 16-7-2 multiplied by 



CHAP. III.] HYDRAULICS. 93 

the load 4 -r- 2 = 16, the effect of the 4 feet head, with 
16 cubic feet expended; because the velocity of the wa- 
ter is 16, and the gate 1 foot. 

Again, suppose it to move by the 16 feet head and 
gate of l-4th of a foot ; then the velocity 32-r-2 multiplied 
by the load 4 -=- 2 = 32, the effect, with but 8 cu- 
bic feet expended, because, the velocity of the water is 
32, and the gate but l-4th of a foot. 

In this case the instant forces are equal, each being 
4 ; but the one moving a body only l-4th as heavy as the 
other, moves with velocity 32, and produces effect 32, 
while the other, moving with velocity 16, produces ef- 
fect 16. A double velocity, with equal instant pressure, 
produces a double effect, which seems to be according 
to the Newtonian theory. And in this sense the mo- 
men turns, of bodies in motion are as their qualities mul- 
tiplied into their simple velocities, and this is what I call 
the instant momentums. 

But when we consider, that in the above case it was 
the quantity of matter put in motion, or water expend- 
ed, that produced the effect, we find that the quantity 
16, with velocity 16, produced effect 16 ; while quantity 
8 with velocity 32, produced effect 32. Here the ef- 
fects are as their quantities, multiplied into the squares 
of their velocities, and this I call the effective momen- 
tums. 

Again, if the quantity expended under each head 
had been equal, their effects would have been 16 and 
64, which is as the squares of their velocities, 16 and 
32. 

4. Again, suppose both wheels to be on one shaft, and 
let a gate of l-8th of a square foot be drawn at 16 C, to 
strike the wheel at K, the head being 16 feet, the instant 
pressure on the gate will be 2 cubic feet of water, which 
is half of the 4 feet head with 1 foot gate, from A 4 
striking at I; but the 16 feet head with instant pres- 
sure 2, acting on the great wheel, will balance 4 feet on 
the small one, because the lever is of double length, and 
the wheels will be in equilibrio. Then, by Waring's 
theory, the greatest load of the 1 6 feet head being 2, its 
load at a maximum will be 1, and the velocity of the wa- 
ter being 32, the maximum velocity of the wheel will be 



94 HYDRAULICS. [CHAP. III. 

16. Now the velocity 16 x 1 = 16, the effect of the 16 
feet head ; and gate of l-8th of a foot, the greatest load 
of the 4 feet head being 4, its maximum load 2, the ve- 
locity of the water 16, and the velocity of the wheel 8 : 
now 8 x 2 = 16, the effect. Here the effects are equal, 
and here, again, the effects are as the instant pressures, 
multiplied into their simple velocities : and the resist- 
ances that would instantly stop them must be equal there- 
to, in the same ratio. 

But when we consider, that in this case the 4 feet 
head expended 16 cubic feet of water, with velocity 16, 
and produced effect 16; while the 16 feet head expend- 
ed only four cubic feet of water, with velocity 32, and 
produced effect 16, we find that the effects are as their 
quantities, multiplied into the squares of their velocities. 

And when we consider, that the gate of l-8th of a 
square foot with velocity 32, produced effects equal to 
the gate of 1 square foot, with velocity 16, it is evident, 
that if we make the gates equal, the effects will be as 8 
to 1; that is, the effects of spouting fluids, with equal 
apertures, are as the cubes of their velocities ; because, 
their instant forces are as the squares of their velocities, 
by'-6th law, although the instant forces of solids are as 
their velocities simply, and their effects as the squares 
of their velocities, a double velocity does not double the 
quantity of a solid body to strike in the same time. 



article 48. 

THE HYDROSTATIC PARADOX. 

The pressure of fluids is as their perpendicular heights, 
without any regard to their quantity; and their pressure 
upAvards is equal to their pressure downwards. In short, 
their pressure is every way equal, at any equal distance 
from their surface. 

In a vessel of cubic form, whose sides and bottom are 
equal, the pressure on each side is just half the pres- 
sure on the bottom ; therefore, the pressure on the bot- 
tom and sides is equal to three times the pressure on the 
bottom. 



CHAP. III.] HYDRAULICS. 95 

And, in this sense, fluids may be said to act with three 
times the force of solids. Solids act by gravity only, 
but fluids by gravity and pressure jointly. Solids act 
with a force proportional to their quantity of matter, but 
fluids act with a pressure proportional to their altitude 
only. 

To explain the law, that the pressure of fluids is as their perpendicular heights, 
let A B C D, Plate III. fig. 22, be a vessel of water of a cubical form, with a 
small tube, as H, fixed therein; let a hole of the same size with the tube be made 
at o, and covered with a piece of pliant leather nailed thereon, so as to hold the 
water. Then fill the vessel with water by the tube H, and it will press upwards 
against the leather, and raise it in a convex form, requiring just as much weight 
to press it down, as will be equal to the weight of the water in the tube H. Or 
if we set a glass tube over the hole at o, and pour water therein, we shall find 
that the water in the tube o, must be of the same height as that in the tube 
H, before the leather will subside, even if the tube o be much larger than H; 
which shows that the pressure upwards is equal To the pressure downwards ; be- 
cause the water pressed up against the leather with the whole weight of the water 
in the tube H. Again, if we fill the vessel by the tube I, it will rise to the same 
height in H that it is in I; the pressure being the same in every part of the vessel 
as if it had been filled by H; and the pressure on the bottom of the vessel will 
be the same, whether the tube H be of the whole size of the vessel, or only one 
quarter of an inch diameter. For suppose H to be l-4th of an inch diameter, and 
the whole top of the vessel of leather, as at o, and we pour water down H, it will 
press the leather up with such force, that it will require a column of water of the 
whole size of the vessel, and height of H, to cause the leather to subside. Q. E. D . 



ARTICLE 49. 



PRACTICAL RESULTS OF THIS EQUAL PRESSURE. 

And again, suppose we make two holes in the vessel, one close to the bottom, 
and the other in the bottom, both of one size, the water will issue with equal ve- 
locity out of each; this maybe proved by holding equal vessels under eaeb, which 
will be filled in equal time; this shows that the pressure on the sides and bottom 
is equal under equal distances from the surface. And this velocity will be the 
same whether the tube be filled by pipe I, or H, or by a tube the whole size of 
the vessels, provided the perpendicular height be equal in all cases. 

From what has been said, it appears, that it makes no difference in the powers 
of water in mill-wheels, whether it be brought on in an open forebay and per- 
pendicular penstock, or down an inclining one, as I C ; or under ground in a close 
trunk, in any form that may best suit the situation and circumstances, provided 
that the trunk be sufficiently large to supply the water fast enough to keep the 
head from sinking. 

This principle of the Hydrostatic Paradox has sometimes operated in undershot 
mills, by pressing up against the bottom of the buckets, thereby destroying or 
counteracting, in great part, the force of impulse. See Art. 59. 



96 HYDRAULICS. [CHAP. III. 



ARTICLE 50. 

The weight of a cubic foot of water is found, by ex- 
perience, to be 1000 ounces avoirdupois, or 62,5 lbs. On 
the principles explained in Art. 48 and 49, is founded the 
following 

THEOREM. 

The area of the base or bottom, or any part of a vessel, 
of whatever form, multiplied by the greatest perpendi- 
cular height of any part of the fluid, above the centre of 
The base or bottom, whatever be its position with the 
horizon, produces the pressure on the bottom of said 
vessel. 



PROBLEM I. 

Given, the length of the sides of the cubic vessel (fig. 
22, PL III.) 6 feet, required the pressure on the bottom 
when full of water. 

Then 6 x 6 = 36 feet, the area, multiplied by 6, the al- 
titude, = 216, the quantity or cubic feet of water, press- 
ing on the bottom ; which multiplied by 62,5 = 13500 lbs. 
the whole pressure on the bottom. 



PROBLEM II. 

Given, the height of a penstock of water, 31,5 feet, 
and its dimensions at bottom 3 by 3 feet inside, required 
the pressure on three feet high of one of its sides, mea- 
suring from the bottom. 

Then, 3 x 3 = 9, the area, multiplied by 30 feet, the 
perpendicular height or head above the centre of the 3 
feet on the side = 270 cubic feet of water pressing, which 
X 62,5= 16875 lbs. the pressure on one yard square, 
which shows what great strength is required to hold the 
water under such great heads. 



ClIAF. III. j HYDRAULICS. 97 

ARTICLE 51. 
RULE FOR FINDING THE VELOCITY OF SPOUTING WATER. 

It has been found by experiment, that water will spout 
from under a 4 feet head, with a velocity equal to 16,2 
feet per second, and from under a 16 feet head, with a ve- 
locity equal to 32,4 feet per second. 

On these experiments, and the 2d law of spouting 
fluids, is founded the following theorem, or general rule, 
for finding the velocity of water under any given head. 

THEOREM. 

As the square root of a 4 feet head (= 2) is to 16,2 feet, 
the velocity of the water spouting under it, so is the 
square root of any other head, to the velocity of the wa- 
ter spouting under it. 

PROBLEM I. 

Given, the head of water 16 feet, required the velo- 
city of water spouting under it. 

Then, as the square root of 4 (== 2) is to 16,2 so is the 
square root of 16, (= 4) to 32,4 the velocity of the water 
under the 16 feet head. 

PROBLEM II. 

Given, a head of water of 11 feet, required a velo- 
city of water spouting under it. 

Then, as 2:16,2::3,316:26,73 feet per second, the ve- 
locity required. 



ARTICLE 52. 

EFFECT OF WATER UNDER A GIVEN HEAD. 

From the 1st and 2d laws of spouting fluids, (Art. 45,) 
the theory for rinding the maximum charge and veloci- 
ty of undershot wheels, (Art. 41,) and from the princi- 

7 



98 HYDRAULICS. [CHAP. III. 

pie of non-elasticity, the following theorem is deduced 
for finding the effect of any gate drawn under any given 
head upon an undershot water wheel. 



THEOREM. 

Find by the theorem (Art. 50,) the instantaneous pres- 
sure of the water, which is the load at equilibrio, and 
2-3ds thereof is the maximum load, which, multiplied by 
,577 of the velocity of the water, under the given head, 
(found by the theorem, Art. 51,) produces the effect. 

PROBLEM. 

Given, the head 16 feet, gate 4 feet wide, ,25 of a 
foot drawn, required the effect of an undershot wheel, 
per second. The measure of the effect to be the quan- 
tity, multiplied into its distance moved (velocity,) or 
into its perpendicular ascent. 

Then, by the theorem (Art. 50) 4 x ,25 = 1 square foot, 
(the area of the gate) x 16 =. 16 the cubic feet pressing ; 
but, for the sake of round numbers, we call each cubic 
foot 1, and although 32,4 cubic feet strike the wheel per 
second, yet, on account of non-elasticity, only 16 cubic 
feet is the load at equilibrio, and 2-6t.hs of 16 is 10,666, 
the maximum load. 

Then, by theorem (Art. 51) the velocity is 32,4 ,577 
of which is = 18,71, the maximum velocity of the wheel 
X 10,66, the load = 199,4, the effect. 

This agrees with Smeaton's observations, where he 
says, (Art. 67,) " It is somewhat remarkable, that though 
the velocity of the wheel in relation to the velocity of 
the water, turns out to be more than l-3d, yet the im- 
pulse of the water, in case of the maximum, is more than 
double of what is assigned by theory; that is, instead of 
4-9 ths of the column, it is nearly equal to the whole co- 
lumn." Hence, I conclude, that non-elasticity does not 
operate so much against this application, as to reduce 
the load to be less than 2-3ds. And when we consider, 
that 32,4 cubic feet of water, or a column 32,4 feet 
long, strikes the wheel, while it moves only 18,71 feet, 



CHAP. III.] HYDRAULICS. 99 

the velocity of the wheel being to the velocity of the 
water as 577 to 1000, may not this be the reason why 
the load is just 2-3ds of the head, which brings the ef- 
fect to be just ,38 (a little more than 1-3 of the power?) 
This I admit, because it agrees with experiment, al- 
though it be difficult to assign the true reason thereof. 
See Annotation, Art. 42. 

Therefore, ,577 the velocity of the water = 18,71, 
multiplied by 2-3ds of 16, the whole column, or instan- 
taneous pressure, pressing on the wheel — Art. 50 — 
which is 10,66 produces 199,4, the effect. This appears 
to be the true effect, and if so, the true theorem will be 
as follows; namely: 



THEOREM. 

Find by the theorem Art. 50, the instantaneous pres- 
sure of the water, and take 2-3ds for the maximum load ; 
multiply by ,577 of the velocity of the water — which 
is the velocity of the wheel — and the product will be the 
effect. 

Then 16 cubic feet, the column, multiplied by 2-3ds 
= 10,66, the load, which multiplied by 18,71, the velo- 
city of the wheel, produces 199,4, for the effect ; and if 
we try different heads and different apertures, we find 
the effects to bear the ratio to each other, that is agree- 
able to the laws of spouting fluids. 



article 53. 

WATER APPLIED ON WHEELS TO ACT BY GRAVITY. 

When fluids are applied to act on wheels to produce ef- 
fects by their gravity, they act on very different princi- 
ples from the foregoing, producing double effects to what 
they do by percussion, and then their powers are direct- 
ly as their quantity, or weight, multiplied into their per- 
pendicular descent. 



100 HYDRAULICS. [CHAP. III. 



DEMONSTRATION. 

Let D. B. fig. 19, Plate III. be a lever, turning on 
its centre or fulcrum A. Let the long arm A B repre- 
sent the perpendicular descent, 16 feet, the short arm 
A D a descent of 4 feet, and suppose water to issue from 
the trunk F, at the rate of 50 lbs. in a second, falling 
into the buckets fastened to the lever at B. Now, from 
the principles of the lever, Art. 16, it is evident, that 
50 lbs. in a second at D, will balance 200 lbs. in a se- 
cond, at D, issuing from the trunk G, on the short arm; 
because 50 x 16 = 800, and 4 x 200 = 800. Perhaps 
it may appear plainer, if we- suppose the perpendicular 
line or diameter F C, to represent the descent of 16 feet, 
and the diameter G I a descent of 4 feet. By the laws 
of the lever — Art. 16 — it is shown that to multiply 50 
into its perpendicular descent 16 feet or distance moved, 
is = 200 multiplied into its perpendicular descent 4 feet, 
or distance moved ; that is, 50 x 16 = 200 x 4 = 800 ; 
that is, their power is as their quantity, multiplied into 
their perpendicular descent; or, in other words, a fall of 
4 feet will require 4 times as much water, as a fall of 16 
feet to produce equal power and effects. Q. E. D. 

Upon these principles is founded the following simple 
theorem, for measuring the power of an overshot mill, 
or of a quantity of water, acting upon any mill-wheel by 
its gravity. 



THEOREM. 

Cause the water to pass along a regular canal, and 
multiply its depth in feet and parts, by its width in feet 
and parts, for the area of its section, which product 
multiply by its velocity per second in feet and parts, 
and the product is the cubic feet used per second, which 
multiplied by 62,5 lbs. the weight of one cubic foot, 
produces the weight of water per second, that falls on 
the wheel, which multiplied by its whole perpendicular 
descent, gives a true measure of its power. 



CHAP. III.] HYDRAULICS. 101 

PROBLEM I. 

Given a mill-seat with 16 feet fall, width of the canal 
5,333 feet, depth 3 feet, velocity of the water passing 
along it 2,03 feet per second, required the power per 
second. 

Then, 5,333 x 3 = 15,999 feet the area of the section 
of the stream, multiplied by 2,03 feet, the velocity, is 
equal 32,4 cubic feet, the quantity per second, multi- 
plied by 62,5 is equal 2025 lbs. the weight of the water 
per second, multiplied by 16, the perpendicular de- 
scent, is equal 32400, for the power of the seat per se- 
cond, 

PROBLEM II. 

Given, the perpendicular descent 18,3 width of the 
gate 2,66 feet, height 1,45 of a foot, velocity of the water 
per second issuing on the wheel, 15,76 feet, required the 
power. 

Then, 2,66 x ,145 = ,3857 the area of the gate, x 15,76 
the velocity = 6,178 cubic feet expended per second, 
x 62,5 = 375,8 lbs. per second, x 18,3 feet perpendicular 
descent = 6877 for the measure of the power per second ; 
which has ground 3,75 lbs. per minute, equal ,375 bush- 
els in an hour, with a five feet pair of burr stones. 



article 54. 

INVESTIGATION OF THE PRINCIPLES OF OVERSHOT MILLS. 

Some have asserted, and many believed, that water 
is applied to great disadvantage on the principle of an 
overshot mill; because, they say, there are never more 
than two buckets, at once, that can be said to act fairly 
on the end of the lever, (as the arms of the wheel are 
called in these arguments.) But we must examine well 
the laws of bodies descending inclined planes, and curved 
surfaces. See Art. 11. This matter will be cleared 
up, if we consider the circumference of the wheel to 



102 HYDRAULICS. [CHAP. III. 

be the curved surface; for the fact is, that the water acts 
to the best advantage, and produces effects equal to what 
it would, in case the whole of it acted upon the very end 
of the lever, in the whole of its perpendicular descent. 
The want of a knowledge of this fact has led to many 
fatal errors in the application of water. 



DEMONSTRATION. 

Let A B C, Plate III. fig. 20, represent a water- 
wheel, and F H a trunk, bringing water to it from a 
16 feet head. Now suppose F G and 16 H to be two 
penstocks under equal heads, down which the water de- 
scends, to act on the wheel at C on the principle of an 
undershot, on opposite sides of the float C with equal 
apertures; it will be evident from the principles of 
hydrostatics, shown by the paradox, (Art. 48, and the 
first law of spouting fluids, Art. 45,) that the impulse 
and pressure, will be equal from each penstock respec- 
tively. Although the one be an inclined plane, and the 
other a perpendicular, their forces are equal, because 
their perpendicular heights are so; (Art. 48,) therefore, 
the wheel will remain at rest, because each side of the 
float is pressed on by a column of water of equal size and 
height, as represented by the lines on each side of the 
float. Then, suppose we shut the penstock F G, and 
let the water down the circular one r x which is close 
to the point of the buckets; this makes it obvious, from 
the same principles, that the wheel will be held in 
equilibria, if the columns of each side be equal. For, 
although the column in the circular penstock is longer 
than the perpendicular one, yet, because part of its 
weight presses on the lower side of the penstock, its 
pressure on the float is due only to its perpendicular 
height. 

Then, again, suppose the column of water in the circu- 
lar penstock to be instantly thrown into the buckets, it 
is evident that the wheel will be still held in equilibrio, 
and each bucket will then bear a proportional part of the 
column that the bucket C bore before ; and that part of 



CHAP. III.] HYDRAULICS. 103 

the weight of the circular column, which rested on the 
under side of the circular penstock, is now on the gud- 
geons of the wheel. This shows that the effect of a 
stream, applied on an overshot wheel, is equal to the ef- 
fect of the same stream, applied on the end of the lever, 
in its whole perpendicular descent, as in fig. 21, where 
the water is shot into the buckets fastened to a strap or 
chain, revolving over two wheels ; and here the whole 
force of the gravity of the column acts on the very end 
of the lever, in the whole of the descent. Although the 
length of the column in action, in this case, is only 16 
feet, whereas, on a 16 feet wheel, the length of the 
column in action is 25,15, yet their powers are 
equal. 

Again, if we divide the half circle into three arches, 
Ab, be, eC, the centre of gravity of the upper and lower 
arches will fall near the point a, 3,9 feet from the cen- 
tre of motion, and the centre of gravity of the middle 
arch, near the point o, 7,6 feet from the centre of mo- 
tion. Now, each of these arches is 8,38 feet, and 8,38 
X 2 x 3,9 = 65,36, and 8,38 x 7,6 feet, = 63,07, which two 
products added = 12S,43, for the momentum of the cir- 
cular column, by the laws of the lever, and for the per- 
pendicular column 16 x 8 the radius of the wheel = 128, 
for the momentum ; by which it appears, that if we could 
determine the exact points on which the arches act, the 
momentums would be equal : all which shows, that the 
power of water on overshot wheels, is equal to the 
whole power it can any way produce, through the whole 
of its perpendicular descent, except what may be lost to 
obtain velocity, (Art. 41,) overcome friction, or by spill- 
ing a part of the water before it gets to the bottom of the 
wheel. Q. E. D. 

I may add, that I have made the following experi- 
ment; namely: I fixed a truly circular wheel on nice pi- 
vots, to avoid friction, and took a cylindrical rod of thick 
wire, cutting one piece exactly the length of half the 
circumference of the wheel, and fastening it to one side, 
close to the rim of the wheel its whole length, as at G x 
r a. I then took another piece of the same wire, of a 
length equal to the diameter of the wheel, and hung it 



104 HYDRAULICS. [CHAP. III. 

on the opposite side, on the end of the lever or arm, as 
at B, and the wheel was in equilibrio. Q. E. D. 



article 55. 

ON THE FRICTION OF THE APERTURES OF SPOUTING FLUIDS. 

The doctrine of this species of friction appears to be 
as follows : — 

1 The ratio of the friction of round apertures, is as 
their diameters, nearly ; while the quantity expended is 
as the squares of their diameters. 

2 The friction of an aperture of any regular or irre- 
gular figure, is as the length 'of the sum of the circum- 
scribing lines, nearly ; the quantities being as the areas 
of the aperture.* Therefore, 

3. The less the head or pressure, and the larger the 
aperture, the less the ratio of the friction; therefore, 

4. This friction need not be much regarded, in the 
large openings or apertures of undershot mills, where the 
gates are from 2 to 15 inches in their shortest sides; but 
it very sensibly affects the small apertures of high over- 
shot or undershot mills, with great heads, where their 
shortest sides are from five-tenths of an inch to twoinches.f 

* This will plainly appear, if we consider that the friction does sensibly re- 
tard the velocity of the fluid to a certain distance; say half an inch'from the side 
or edge of the aperture, towards its centre ; and we may reasonably conclude, that 
this distance will be nearly the same in a 2 and 12 inch aperture ; so that in the 
2 inch aperture, a ring on the outside, half an inch wide, is sensibly retarded, 
which is about 3-4ths of the whole: while, in the 12 inch aperture, there is a ring 
on the outside half an inch wide, retarded about one sixth of its whole area. 

f This seems to be proved by Smeaton, in his experiments; (see table, Art. 67;) 
where, when the head was 33 inches, the sluice small, drawn only to the 1st hole, 
the velocity was only such as is assigned by theory to a head of 15,85 inches, 
which he calls virtual head. But when the sluice was larger, drawn to the 6th 
hole, and head 6 inches, the virtual head was 5,33 inches. But seeing there is no 
theorem, yet discovered, by which we can truly determine the quantity or effect of 
the friction, according to the size of the aperture, and height of the head; we can- 
not, therefore, by the established laws of hydrostatics, determine exactly the velo- 
city or quantity expended through any small aperture; which renders the theory 
in these cases but little better than conjecture. 



CHAP. III.] HYDRAULICS. 105 

ARTICLE 56. 
OF THE PRESSURE OF THE AIR ON FLUIDS. 

Under certain circumstances, the rise of water is 
caused by the pressure of the air on the surface of its 
reservoir, or source.; and this pressure is equal to that of 
a head of water of about 33J feet perpendicular height ; 
under which pressure or height of head, the velocity of 
spouting water is 46,73 feet per second. 

If, therefore, we could by any means take off the pres- 
sure of the atmosphere, from any one part of the surface 
of a fluid, that part would spout up with a velocity of 
46,73 feet per second, and rise to the height of 33 J feet 
nearly. 

All syphons, or cranes, and all pumps for raising wa- 
ter by suction, as it is called, act on this principle. — Let 
fig. 23, PI. III. represent a cask of water, with a syphon 
therein, to extend 33J feet above the surface of the wa- 
ter in the cask. Now, if the bung be made perfectly 
air-tight round the syphon, so that no air can get into 
the cask, and the cask be full, and if all the air be then 
drawn out of the syphon, the fluid will not rise in the 
syphon, because the air cannot get to it to press it up ; 
but take out the plug P, and let the air into the cask, 
to press on the surface of the water, and it will spout up 
the short leg of the syphon B A, with the same force 
and velocity, as if it had been pressed with a head of 
water 33^ feet high, and will run into the long leg and 
fill it. If we then turn the cock c, and let the water 
run out, its weight in the long leg will overbalance the 
weight in the short one, drawing the water out of the 
cask until it sinks so low, that the leg B A will be 33 J 
feet high, above the surface of the water in the cask ; it 
will then stop, because the weight of water in the legs, 
in which it rises, will be equal to the weight of a column 
of the air of equal size, and of the whole height of the 
atmosphere. The water will pot run out of the leg A 
C, but will stand 33J feet above its mouth, because the 
air will press up the mouth C, with a force that will 



106 HYDRAULICS. [CHAP. III. 

balance 33 J feet of water in the leg C A. This will be 
the case let the upper part of the leg be of any size what- 
ever — and there will be a vacuum at the upper end of the 
syphon. 

It must not, however, be supposed that if the mouth 
C be left open, after the water has ceased running, that 
the portion of it which is in the leg A C, will remain 
there, as air will be gradually admitted, and will press 
upon the upper end of the column A B, which will then 
descend in both legs. 



article 57. 



OF PUMPS. 



Let fig. 24, PI. III. represent a pump of the common 
kind used for drawing water out of wells. The moveable 
valve or bucket A, is cased with leather, which springs 
outwards, and fits the tube so nicely, that neither air nor 
water can pass freely by it. When the lever L is worked, 
the valve A opens as it descends, letting the air or wa- 
ter pass through it. As it ascends again, the valve shuts, 
the water which is above the bucket A is raised, and 
there would be a vacuum between the valves, but the 
weight of the air presses on the surface of the water in 
the well, at W, forcing it up through the valve B, to fill 
the space between the buckets; and as the valve A de- 
scends, B shuts, and prevents the water from descending 
again. But if the upper valve A be set more than 33J 
feet above the surface of the water in the well, the pump 
cannot be made to draw, because the pressure of the at- 
mosphere will not cause the water to rise more than 33J 
feet. Although in theory the water would rise to the 
height stated, yet in point of fact, the distance between 
the valve in the piston, and the surface of the water in 
the well, ought never to exceed 24 or 25 feet, or, from 
the imperfection of workmanship, and other causes, the 
pump will lose water; and will cease to act. 



CHAP. lit.] 



HYDRAULICS. 



107 



A TABLE FOR PUMP MAKERS. 







Diameter of 


Water discharged 


Height of 


the 


the bore 


in a minute, in 


pump, in 


feet, 


O l— 


wine measure. 


above the 


sur- 


3" "*><=> 

— C3 O 




face of 


the 




Q ""d 


well. 




en 5' § 


ints. 

alls. 


10 




6 93 


81 6 


15 




5 66 


54 4 


20 




4 90 


40 7 


25 




4 38 


32 6 


30 




4 00 


27 2 


35 




3 70 


23 3 


40 




3 46 


20 3 


45 




3 27 


18 1 


50 




3 10 


16 3 


55 




2 95 


14 7 


60 




2 84 


13 5 


65 




2 72 


12 5 


70 




2 62 


11 4 


75 




2 53 


10 7 


80 




2 45 


10 2 


85 




2 38 


9 5 


90 




2 31 


9 1 


95 




2 25 


8 5 


100 




2 18 


8 1 



The preceding table is extracted from Ferguson's Lectures, and its use is pointed 
out by him in the subjoined quotation: before giving which, however, it will be 
proper to remark, that it is a common practice to make the bore in the lower part 
of the pump-tree smaller than the chamber, under the erroneous supposition that 
there will be a less weight of water to lift in this than in a larger bore. The con- 
sequence of this is, that the water has to rush with greater velocity in order to 
fill the capacity of the chamber, by which much friction is caused, and much power 
wasted. 

"All pumps should be so constructed as to work with equal ease in raising the 
water to any given height above the surface of the well : and this may be done by 
observing a due proportion between the diameter of that part of the pump-bore in 
which the piston or bucket works, and the height to which the water must be 
raised. 

"For this purpose I have calculated the above table ; in which the handle of 
the pump is supposed to be a lever, increasing the power five times : that is, the 
distance or length of that part of the handle that lies between the pin on which it 
moves, and the top of the pump rod to which it is fixed, to be only one-fifth part 
of the length of the handle, from the said pin to the part where the man who 
works the pump applies his force or power. 

"In the first column of the table, find the height at which the pump must dis- 
charge the water above the surface of the well: then in the second column you 
have the diameter of that part of the bore in which the piston or bucket works, in 
inches and hundredth parts of an inch; in the third column is the quantity of 
water (in wine measure) that a man of common strength can raise in a minute — 
And by constructing according to this method, pumps of all heights may be 
wrought for a man of ordinary strength, so as to be able to hold out for an hour." 



10S HYDRAULICS. [CHAP. II!. 

/ 

ARTICLE 58. 

OF CONVEYING WATER UNDER VALLEYS AND OVER HILLS. 

Water, by its own pressure, and the pressure of the at- 
mosphere, may be conveyed under valleys and over hills, 
to supply a family, a mill, or a town. In fig. 20, PI. 
III. F H is a canal for conveying water to a mill-wheel : 
now let us suppose F G 16 H to be a tight tube or trunk, 
— the water being let in at F, it will descend from F to 
G, and its pressure at F will cause it to rise to H, which 
shows how it may be conveyed under a valley ; and it 
may be conveyed over a hill, by a tube, acting on the 
principle of the syphon. (Art. 56.) But some who have 
had occasion to convey water, under any obstacle, for 
the convenience of a mill, have gone into the following 
expensive error; they have made the tube at G 16, 
smaller than they would if it had been on a level; because, 
say they, a greater quantity will pass through a tube, 
pressed by the head G F, than on a level; but, it should 
be considered that the head G F, is balanced by the 
hea'd H 16, and the velocity through the tube G 16, will 
be such only, as a head equal to the difference between 
the perpendicular height of G F, and H 16, would give 
it (see Art. 41, fig. 19 ;) therefore, it should be as large 
at G 16; as if on a level. 



article 59. 

OF THE DIFFERENCE IN THE FORCE OF INDEFINITE AND DEFINITE 
QUANTITIES OF WATER STRIKING A WHEEL. 

DEFINITIONS. 

1. By an indefinite quantity of water we here mean a 
river, or quantity much larger than the float of the wheel, 
so that, when it strikes the float, it has liberty to move 
or escape from it in every lateral direction. 

2. By a definite quantity of water we mean a quantity 



CHAP. III.] HYDRAULICS. 109 

passing through a given aperture, along a shute, to 
strike a wheel; but as it strikes the float, it has liberty 
to escape in every lateral direction. 

3. By a perfectly definite quantity we mean a quan- 
tity passing along a close tube, so confined that when it 
strikes the float, it has not liberty to escape in any late- 
ral direction. 

First, When a float of a wheel is struck by an indefi- 
nite quantity, the float is struck by a column of water, 
the section of which is equal to the area of the float; and 
as this column is confined on every side by the surround- 
ing water which has equal motion, it cannot escape 
sideways without some resistance; more of its force, there- 
fore, is communicated to the float, than would be, if it 
had free liberty to escape in every direction. 

Secondly, The float being struck by a definite quan- 
tity with liberty to escape freely in every lateral direc- 
tion, it acts as the most perfectly non-elastic body; there- 
fore (by Art. 9) it communicates only a part of its force, 
the other part being spent in the lateral direction. 
Hence it appears, that in the application of water to 
act by impulse, we should draw the gate as near as possi- 
sible, to the float-board, and confine it as much as possi- 
ble from escaping sideways as it strikes the float ; 
but taking care, at the same time, that we do not bring 
the principle of the Hydrostatic Paradox into action. 
(Art. 48.) 

What proportion of the force of the water is spent in 
a lateral direction is not determined. 

4. A perfectly definite quantity striking a plane, 
communicates its whole force, because no part can escape 
sideways ; and is equal in power to an elastic body, or to 
the weight of the water on an overshot wheel, in its 
whole perpendicular descent. But this application of 
water to wheels in this way, has hitherto proved imprac- 
ticable; for whenever we attempt to confine the water, 
totally from escaping sideways, we bring the principle 
of the hydrostatic paradox into action, which defeats the 
scheme. 

To make this plain, let fig. 25, PI. III. be a water- 
wheel, and, first, let us suppose the water to be brought 



110 HYDRAULICS. [ CHAP. III. 

to it, the penstock 41.6, to act by impulse on the float 
board, having liberty to escape, every way as it strikes; 
then, by Art. 9, it will communicate but half its force. 
But if it be confined both at the sides and bottom, 
and can escape only upwards, to which the gravity 
will make some opposition, it will communicate more 
than half its force, and will not react back against the 
float C; but if we put soaling to the wheel, to prevent 
the water from escaping upwards, then the space between 
the floats will be filled as soon as the wheel begins to be 
retarded, and the paradoxical principle, Art. 48, is 
brought fully into action; namely: the pressure of water 
is every way equal; and it will press backwards against 
the bottom of the float C, with a force equal to its pres- 
sure on the top of the float b, and the wheel will imme- 
diately stop, and be held in equilibrio, and will not start 
again although all resistance be removed. There are 
many mills, where this principle is, in part, brought into 
action, which very much lessens their power. 



ARTICLE 60. 
OF THE MOTION OF BREAST AND PITCH-BACK WHEELS. 

Many have been of opinion, that when water is put to 
act on a low breast wheel, as at a, (PL 3, fig. 25,) with 
12 feet head, that then the four feet fall, below the point 
of impact a, is totally lost, because, say they, the impulse 
of the 12 feet head will require the wheel to move with 
such velocity to suit the motion of the water, as to move 
before the action of gravity, therefore, the water cannot 
act after the stroke; but if they will consider well the 
principles of gravity acting on falling bodies, (Art. 10,) 
they will find, that if the velocity of a falling body be 
ever so great, the action of gravity to cause it to move 
faster is still the same; so that, although an overshot wheel 
may move before the power of the gravity of the water 
thereon, yet no impulse downwards can give a wheel such 



CHAP. III.] HYDRAULICS. Ill 

velocity, as that the gravity of the water acting thereon 
can be thereby lessened.* 

Hence, it appears, that when a greater head is used 
than that which is necessary to shoot the water fairly 
into the wheel, the impulse should be directed a little 
downward, as at D, (which is called pitch-back,) and it 
should have a circular sheeting, to prevent the water 
from leaving the wheel; because if it be shot horizontally 
on the top of the wheel, the impulse in that case will not 
give the water any greater velocity downwards, and, in 
this case, the fall would be lost, if the head were very 
great: and if the wheel moved to suit the velocity of the 
impulse, the water would be thrown out of the buckets 
by the centrifugal force; and if we attempt to retard the 
wheel so as to retain the water, the mill would be so 
ticklish and unsteady, that it would be almost impossible 
to attend it. 

Hence may appear the reason why breast-wheels ge- 
nerally run quicker than overshots, although the fall, 
after the water strikes, be not so great. 

1. There is generally more head allowed to breast- 
wheels than to overshots; and the wheel will incline to 
move with nearly 2-3ds the velocity of the water spout- 
ing from under the head. (Art. 41.) 

2. If the water were permitted to fall freely after it 
issues from the gate, it would be accelerated by the fall, 
so that its velocity at the last point would be equal to its 
velocity had it. spouted from under a head equal to its 
whole perpendicular descent. This accelerated veloci- 
ty of the water tends to accelerate the wheel ; hence, to 
find the velocity of a breast wheel, where the water 
strikes it in the direction of a tangent, as in fig. 31, 32, I 
deduce the following 

* If gravity could be either decreased by velocity downwards or increased by 
velocity upwards, then a vertical wheel without friction, either of gudgeons or air, 
would require a great force to continue its motion; because its velocity would de- 
crease the gravity of its descending and increase that of its ascending side, which 
would immediately stop it ; whereas, it is known that it requires no power to 
continue its motion, but that which is necessary to overcome the friction of the 
gudgeons, &c. 



112 HYDRAULICS. [c'HAP. III. 



THEOEEM. 

1. Find the difference of the velocity of the water 
under the head allowed to the wheel, above the point 
of impact, and the velocity of a body, having fallen the 
whole perpendicular descent of the water. Call this 
difference the acceleration by the fall : Then say, As 
the velocity a body would acquire in falling through the 
diameter of any overshot wheel, is to the proper veloci- 
ty of that wheel by the scale, (Art. 43,) so is the acce- 
leration by the fall of the water before it strikes the 
wheel, to the acceleration of the wheel by its fall, after 
it strikes. 

2. Find the velocity of ,the water issuing on the 
wheel; take, 577 of said velocity, to which add the ac- 
celerated velocity, and that sum will be the velocity of 
the breast-wheel. 

This rule will hold nearly true, when the head is con- 
siderably greater than is assigned by the scale, (Art. 43;) 
but as the head approaches that assigned by the scale, 
this rule will give the motion too quick. 

EXAMPLE. - 

Given, a high breast-wheel, fig. 25, where the water 
is shot on at D, the point of impact — 6 feet head, and 
10 feet fall — required the motion of the circumference 
of the wheel, working to the best advantage, or maxi- 
mum effect. 
The velocity of a falling body, having 16 ^ n ) r . 

feet fall, the whole descent, ^ ' 

Then the velocity of the water, issuing ,q„, ■. 

on the wheel, 6 feet head, } " ' 



irence, - 13,06, do. 

Then as the velocity under a 16 feet fall (32,4 feet) 
is to the velocity of an overshot wheel = 8,76 feet, so is 
13,06 feet, to the 16 feet diameter velocity accelerated, 
which is equal 3,5 feet, to which add, 577 of 19,34 feet, 
(being 11, 15 feet;) and this amounts to 14,65 feet per se- 
cond, the velocity of the breast-wheel. 



CHAP. III.] HYDRAULICS. 113 

ARTICLE 61. 

RULE FOR CALCULATING THE POWER OF ANY MILL-SEAT. 

The only loss of power sustained by using too much 
head, in the application of water to turn a mill-wheel, 
is from the head producing only half its power. There- 
fore, in calculating the power of 16 cubic feet per se- 
cond on the different applications of fig. 25, PI. III. 
we must add half the head to the whole fall, and count 
that sum the virtual perpendicular descent. Then, by 
the theorem in Art. 53, multiply the weight of the wa- 
ter per second by its perpendicular descent, and you 
have the true measure of its power. 

But to simplify the rule, let us call each cubic foot 1, 
and the rule will then be — Multiply the cubic feet ex- 
pended per second, by its virtual perpendicular descent 
in feet, and the product will be a true measure of the 
power per second. This measure must have a name, 
which I call Cuboch : that is, one cubic foot! of water, 

' * fife 7 

multiplied by one foot descent, is one cuboch, or the 
unit of power. 

EXAMPLES,.] 

1. Given, 16 cubic feet of water per second, to be ap- 
plied by percussion alone, under 16 feet head, required 
the power per second. 

Then, half 16 = 8 x 16 = 128 cubochs, for the mea- 
sure of the power per second. 

2. Given, 16 cubic feet per second, to be applied to 
a half breast of 4 feet fall and 12 feet head, required the 
power. 

Then, half 12 = 6 + 4 = 10 x 16 = 160 cubochs for 
the power. 

3. Given, 16 cubic feet per second, to be applied to a 
pitch-back or high-breast — fall 10, head 6 feet, required 
the power. 

8 



114 HYDRAULICS. [CHAP. III. 

Then, half 6 = 3 + 10 = 13 x 16 = 208 cubochs, for 
the power per second. 

4. Given, 16 cubic feet of water per second, to be ap- 
plied as an overshot — head 4, fall 12 feet, required the 
power. 

Then, half 4 = 2 + 12 = 14 x 16 = 224 cubochs, for 
the power. 

The powers of equal quantities of water amounting to 
16 cubic feet per second, the total perpendicular de- 
scents being equal, stand thus by the different modes of 
application: 

(16 feet head,* 
The undershot, < fall, 

(128 cubochs of power. 
C 12 feet head, 
The half breast, < 4 feet fall, 

(160 cubochs of power. 
I 6 feet head, 
The high breast, < 10 feet fall, 

( 208 cubochs of power. 
C 4 feet head, 
The overshot, 2 12 feet fall, 

( 224 cubochs of power. 
I 2,5 feet head, 
Ditto, ?31,5 feet fall, 

( 263 cubochs of power. 
The last being the head necessary to shoot the water 
fairly into the buckets, may be said to be the best appli- 
cation. See Art. 43. 

On these simple rules, and the rule laid down in Art. 
43, for proportioning the head and fall, I have calcu- 

r * Water, by percussion, spends its force on the wheel in the following time, 
which is in proportion to the distance apart of the float-boards and the difference 
of the velocity of the water and the wheel. 

If the water runs with double the velocity of the wheel, it will spend all its force 
on the floats while the water runs to the distance of two float-boards, and while 
the wheel funs to the distance of one ; therefore, the water need not be kept to act 
on the wheel farther from the point of impact than the distance of about two float- 
boards. 

But if the wheelrun with two-thirds of the velocity of the water, then, while 
the wheel runs the distance of two float, and while the water would have run the 
distance of three float, it spends all its force ; therefore, the water need be kept 
to act on the wheel the distance of three floats only past the point of impacts. 

If it be continued in action much longer, it will fall back, and re-act against 
the following bucket, and retard the wheel. 



CHAP. III.] 



HYDRAULICS. 



115 



lated the following table, or scale, of the different quan- 
tities of water expended per second, with different per- 
pendicular descents, to produce a certain power; in or- 
der to present, at one view, the ratio of increase or de- 
crease of quantity, as the perpendicular descent increases 
or decreases. 



A TABLE 

Showing the quantity of water required, with different falls, to produce, hy its 
gravity, 112 cubochs of power, which will drive a five feet stone about 97 revo- 
lutions in a minute, grinding about five bushels of wheat in an hour. 



The vir 
water 
added 
it strik 


" C 

'-s E. 


The vir 
water, 
added 
it strik 


" s 

Cfl o 

" CD 1 


(t ?ETr* 


O CD 


» fT tfrt 


O (D 


w ° cd a 


B t+ 


»°of 


B rt- 


Effl S i — 


P-o 


Sp 5'i 


P-o 


desc 
g hal 
.11 the 
tie wh 


!-^> 
3 




►"-l 
3 


P 


P 


rt> l "*> CD 


CD 


CD lv T> CD 


CD 


nt o 
the 
fall, 

el. 


l-S 
CD 


i-. m o 


CD 
,£5 


» ^^ 


C_ 


»= 5""* 


g; 




CD 


**a CD 


CD 


►3 ~ cd 


P- 


>-S u CD 


&. 


1 


112 


16 


7 


2 


56 


17 


6.58 


3 


37.3 


18 


6.22 


4 


28 


19 


5.99 


5 


22.4 


20 


5.6 


6 


18.6 


21 


5.33 


7 


16 


22 


5.1 


8 


]4 


23 


4.87 


9 


12.4 


24 


4.66 


10 


11.2 


25 


4.48 


U 


10.2 


26 


4.3 


12 


9.33 


27 


4.15 


13 


8.6 


28 


4 


14 


8 


29 


3.86 


15 


7.46 


30 


3.73 



>* 



ARTICLE 62. 



THEORY AND PRACTICE COMPARED. 

I will here give a table of 18 mills in actual practice, 
out of about 50 of which I have taken an account, in or- 
der to compare theory with practice, and in order to as- 



116 HYDRAULICS. [CHAP. III. 

certain the power required on each superficial foot of the 
acting parts of the stone. But I must premise the fol- 
lowing 



THEOREMS. 

1. To find the circumference of any circle, as of a 
mill-stone, by the diameter, or the diameter by the cir- 
cumference; say, 

As 7 is to 22, so is the diameter of the stone to the 
circumference; that is, multiply the diameter by 22, and 
divide the product by 7, for the circumference; or mul- 
tiply the circumference by 7, and divide the product by 
22, for the diameter. 

2. To find the area of a circle, by the diameter: As 
1, squared, is to ,7854, so is the square of the diameter 
to the area; that is, multiply the square of the diameter 
by ,7854, and, in a mill-stone, deduct one foot for the 
eye, and you have the area of the stone. 

3. To find the quantity of surface passed by a mill- 
stone: The area, squared, multiplied by the revolutions 
of. the stone, gives the number of superficial feet, passed 
in a given time. 



OBSERVATIONS ON THE FOLLOWING TABLE OF EXPERIMENTS. 

I have asserted, in Art. 44, that the head above the 
gate of a wheel, on which the water acts by its gravity, 
should be such, as to cause the water to issue on the 
wheel, with a velocity to that of the wheel, as 3 to 2. 
Compare this with the following table of experiments. 

1. Exp. Overshot. Velocity of the water 12,9 feet 
per second, velocity of the wheel 8,2 feet per second, 
which is a little less than2-3ds of the velocity of the wa- 
ter. This wheel received the water well. It is at Stan- 
ton, in Delaware state. 

2. Overshot. Velocity of the water 11,17 feet per se- 
cond, 2-3ds of which is 7,44 feet; velocity of the wheel 
,85 feet per second. This received the water pretty 
well. It is at the above-mentioned place. 



CHAP. III.] HYDRAULICS. 117 

3. Overshot. Velocity of the water 12,16 feet per 
second, velocity of the wheel 10,2; throws out great part 
of the water by the back of the buckets, which strikes it, 
and makes a thumping noise. It is allowed to run too 
fast; revolves faster than my theory directs. It is at 
Brandywine, in Delaware state. 

4. Overshot. Velocity of the water 14,4 feet per se- 
cond, velocity of the wheel 9,3 feet, a little less than 
2-3ds of the velocity of the water. It receives the wa- 
ter very well; has a little more head than assigned by 
theory, and runs a little faster; it is a very good mill, si- 
tuated at Brandywine, in the state of Delaware. 

6. Undershot. Velocity of the wheel, loaded, 16, 
and when empty, 24 revolutions per minute, which con- 
firms the theory of motion for undershot wheels. See 
Art. 42. 

7. Overshot. Velocity of the water 15,79 feet, velo- 
city of the wheel 7,8 feet; less than 2-3ds of the velocity 
of the water; motion slower and head more than as- 
signed by theory. The miller said the wheel ran too 
slowly, that he would have it altered ; and that it worked 
best when the head was considerably sunk. This mill is 
at Bush, Hartford county, Maryland. 

8. Overshot. Velocity of the water 14,96 feet per se- 
cond, velocity of the wheel 8,8 feet, less than 2-3ds, 
very near the velocity assigned by the theory; but the 
head is greater, and the wheel runs best when the head 
is sunk a little ; is counted the best mill, and is at the 
same place with the last mentioned. 

9. 10, 11, 12. Undershot open wheels. Velocity of 
the wheels when loaded 20 and 40, and when empty 28 
and 56 revolutions per minute, which is faster than my 
theory for the motion of undershot mills. Ellicott's 
mills, near Baltimore, in Maryland, serve to confirm the 
theory. 

14. Overshot. Velocity of the water 16,2 feet, velo- 
city of the wheel 9,1 feet, less than 2-3ds of the water, 
revolutions of the stone 144 per minute, the head nearly 
the same as by theory, the velocity of the wheel less, 
stone more. This shows the mill to be geared too high. 



118 HYDRAULICS. [cHAP. III. 

The wheel receives the water well, and the mill is 
counted a very good one, situated at Alexandria, in 
Virginia. 

15. Undershot. Velocity of the water, 24,3 per se- 
cond, velocity of the wheel ] 6,67 feet, more than 2-3ds 
the velocity of the water. Three of these mills are in 
one house, at Richmond, Virginia — they confirm the 
theory of undershots, being very good mills. 

16. Undershot. Velocity of the water 25,63 feet per 
second, velocity of the wheel 19,05 feet, being more than 
2-3ds. Three of these mills are in one house, at Peters- 
burg, in Virginia — they are very good mills, and confirm 
the theory. See Art. 43. 

18. Overshot wheel. Velocity of the water 11,4 feet 
per second, velocity of the wheel 10,96 feet, nearly as 
fast as the water. The backs of the buckets strike the 
water, and drive a great part over,* and as the motion of 
the stone is about right, and the motion of the wheel 
faster than assigned by the theory, it shows the mill to 
be too low geared, all which confirm the theory. See 
Art. 43. 

In the following table I have counted the diameter of 
tire mean circle to be 2-3ds of the diameter of the great 
circle of the stone, which is not strictly true. The mean 
circle to contain half the area of any given circle, must 
be ,707 parts of the diameter of the said circle, differing 
but little from ,7, and somewhat exceeding 2-3ds. 

Hence the following theorem, for finding the mean cir- 
cle of any stone. 

THEOREM. 

Multiply the diameter of the stone by ,707, and the 
product is the diameter of the mean circle. 

EXAMPLE. 

Given, the diameter of the stone 5 feet, required a 
mean circle that shall contain half its area. 

Then 5 x ,707 = 3,535 feet, the diameter of the mean 
circle. 



CHAP. III.] HYDRAULICS. 119 

ARTICLE 63. 

FARTHER OBSERVATIONS ON THE FOLLOWING TABLE. 

1. The mean power used to turn the 5 feet stones in 
the experiments (No. 1, 7, 14, 17,) is 87,5 cubochs of 
the measure established, Art. 61, and the mean velocity 
is 104 revolutions of the stones in a minute, the velocity 
of the mean circle being 18,37 feet per second, and their 
mean quantity ground is 3,8 lbs. per minute, which is 
3,8 bushels per hour, and the mean power used to each 
foot of the area of the stone is 4,69 of the measure afore- 
said, effected by 36582 superficial feet, passing each 
other in a minute. Hence we may conclude, 

1. That 87,5 cubochs of power per second will turn 
a 5 feet stone, 104 revolutions in a minute, and grind 
3,8 bushels in an hour. 

2. That 46,9 cubochs of power are required to every 
superficial foot of a mill-stone, when its mean circle 
moves with a velocity of 18,37 feet per second. Or, 

3. That for every 36582 feet of the face of stones that 
pass each other, we may expect 3,8 lbs. will be ground, 
when the stones, grain, &c, are in the same state and 
condition as they were in the above experiments. 



120 



HYDRAULICS. 



[CHAP. III. 



A TABLE OF EXPERIMENTS ON EIGHTEEN MILLS IN PRACTICE. 



Quantity ground per 
minute in lbs. or per 
hour in busliels. 




3.5 

2.5 

3.75 

4.5 
3.5 


Superficial feet passed 
in a minute. 




34594 
21514 

36435 
35741 
108091 

36435 

36435 

95264 
49678 
49558 

71850 
35741 


Velocity of the mean 
circle. 


S3 


17.3 
18.5 

16.97 
18.6 

18.32 
17.97 
17.94 

18.32 

18. 32 

16.92 
16.89 
19.89 
20. 75 
19.9 
17.97 


Power required to each 
foot of face. 




4.1 
4.34 

4.9 
5.9 

4.67 
5.15 


Area of the stones. 


a. 


18.63 
13.13 

18.63 
18.63 

38.48 

18.63 

36.63 
23.76 
18.63 

28.38 
18.63 


Diameter of stones in 
feet and inches. 


c 


ncitoocon 2 2to ■* tt oo 
lO-^-f^-^^^ mint* m •*? in (DonifltDio^? 


Revolutions of the 
stones per minute. 




t^oo 

oS ■* cm e? ■■* oo to in co co m m m HcotMinn-a-a 
03 £! 2 S 2 2 £ ! ' 22^ 2 ° ° f» S A — SoSS 


Rounds in trundles. | 2 — 22! — -2 ^S 1 " 2 2 2 222^™— 2 co 


Cogs in the counter 1 
cog-wheels. 


Tf CO ■* Tf rt< Tf CO ■*■* •*Tf! T *' TfOOuL. 


Rounds in the wal- 1 
loweis. 


r~ cm xt> -<? -* co cm cm cm mo co to 

CM CM CM CM Si CM CX CX <N CM CM CM CI C! CM 


Number of cogs in the 1 
master-wheel. 


co oo ©t to ©J OO CM-* CM rf C* tO to © -S< CO CM 

oucot» to f- r>. r- oo ^ oo v o os to Tf to r-. 


Velocity of circumfe- 
rence per second. 




8.2 
8.5 
10.2 

9.3 

9.8 
loaded 
unloaded 

7.8 

8.8 
loaded 
unloaded 
loaded 
unloaded 
loailed 
unloaded 
loaded 
unloaded 

7.8 

9.1- 
16.67 
19 05 

9.2 
10.96 


Number of Revolutions 
per minute. 




oo oi co 'cm "oto-^crioooootoooootoooo cm m to •# 

,-, w — iH CM — & CM -3" O CM ~> -T m CO •* — -^ 


- 

Diameter of wheel. 


■1 


r~ ^ ■* in m to co 

00 CO UO IC t t^ .tOtOtOUO ^ 111 N 33 cicCO-^ 1 


Power per sec. by sim- 
ple theorem. Art. 61. 


1 


to r-- wo to to 
i* to ... . . C3 *H . . . • . OC . .Oi 


Cub. ft. expended per 
sec. abating for fric- 
tion by conjecture. 


O 


3.8 
3.5 

5. 18* 
6.16 

3.57 
7.6 " 


Velocity of water per 
second, by theory. 


- 


12.9 
11.17 
12.16 
14.4 

13 .8 

15. 79 
14.96 
26.73 

16.2 

16.2 
24.3 
i5 63 
14 
11.4 


Area of gate, abating 
for contraction occa- 
sioned by friction. 


c£ 


in uo ioin ' t» 
oo cm -*r ex to 
CO CO CO ■* in 


Head above the centre 
of the gate. 


cu 


caul h com.... .. 

CM "CM CO CO COCO ■^C'S" con 


Virtual or effective de- 
scent of water. 


Cm 


20. 

19.2 

16.2 

16.6 

19.25 

17.8 
17.8 

20.6 

21.5 
9.5 
10 
12.5 


Vo. of experiments. | | <-<«« -* w tot-oocn o £ w n 2«»too 



In the 3d, 4th, 13th, and 18th experiments, in the above table, there are two pair 
of stones to one water-wheel, the gears, &c. of which are shown by the braces. 



CHAP. III.] HYDRAULICS. 121 

Observations continued from page 111. 

As we cannot attain to a mathematical exactness in 
those cases, and as it is evident that all the stones in the 
foregoing experiments have been working with too little 
power, because it is known that a pair of good burr stones 
of 5 feet diameter will grind, sufficiently well, about 125 
bushels in 24 hours— that is, 5,2 bushels in an hour, which 
would require 6,4 of power per second — we may, for the 
sake of simplicity, say 6 cubochs, when 5 feet stones 
grind 5 bushels per hour. Hence we deduce the follow T - 
ing simple theorem for determining the size of the stones 
to suit the power of any given seat, or the power required 
to any size of a stone. 

THEOREM. 

Find the power by the theorem, in Art. 61; then di- 
vide the power by 6, which is the power required, by 1 
foot, and it will give you the area of the stone that the 
power will drive, to which add 1 foot for the eye, and di- 
vide by ,7854, and the quotient will be the square of the 
diameter : or, if the pow r er be great, divide by the pro- 
duct of the area of any sized stones you choose, multi- 
plied by six, and the quotient will be the number of stones 
the power will drive: or, if the size of the stone be given, 
multiply the area by 6 cubochs, and the product is the 
power required to drive it. 

EXAMPLE. 

1. Given, 9 cubic feet per second, 12 feet perpendicu- 
lar, virtual, or effective descent, required the diameter of 
the stone suitable thereto. 

Then, by Art. 61, 9x12= 108, the power, and 108 -^- 
6 = 18, the area, and 18 x 1 -h- ,7854 = 24,2, the root of 
which is 4,9 feet, the diameter of the stone required. 

2. The velocities of the mean circles of the stones in 
the table, are some below and some above 18 feet per se- 
cond, the mean of them all being nearly 18 feet; there- 
fore, I conclude that 18 feet per second is a good veloci- 
ty, in genera], for the mean circle of any sized stone. 



122 HYDRAULICS. [CHAP. III. 

Of the different quantity of Surfaces that are passed by 
Millstones of different diameters with different veloci- 
ties. 

Supposing the quantity ground by mill-stones, and the 
power required to turn them, to be as the passing sur- 
faces of their faces, each superficial foot that passes over 
another foot requires a certain power to grind a certain 
quantity : to explain this, let us premise, 

1. The circumferences and diameters of circles are di- 
rectly proportional. That is, a double diameter gives a 
double circumference. 

2. The areas of circles are as the squares of their di- 
ameters. That is, a double a'iameter gives 4 times the 
area. 

3. The square of the diameter of a circle, multiplied 
by ,7854, gives its area. 

4. The square of the area of a mill-stone, multiplied 
by its number of revolutions, gives the surface passed. 
Consequently, 

5. In stones of unequal diameters, revolving in equal 
times, their passing surfaces, quantity ground, and power 
required to drive them, will be as the squares of their 
areas, or as the biquadrate of their diameters. That is, 
a double diameter will pass 16 times the surface.* 

6. If the'velocity of their mean circles or circumfe- 
rences be equal, to their passing surfaces, quantity ground, 
and power required to move them, will be as the cubes 
of their diameters.t 

7. If the diameters and velocities be unequal, their 
passing surfaces, and quantity ground, &c, will be as 



* The diameter of a 4 feet stone squared, multiplied by .7854, equal 12,56, its 
area; which squared is 157,75 feet, the surface passed ai one revolution: and 8 
multiplied by 8 equal 64, which multiplied by ,7S54, equal 50,24, being the area of 
an 8 feet stone; which squared is 2524,04, the surface passed, which surfaces are 
as 1 to 16. 

t Because the 8 feet stone will revolve only half as often as the 4 feet ; therefore, 
their quantity of surface passed, &c, can only be half as much more as it was in 
the last case ; that is, as 8 to 1 . 



CHAP. III.] HYDRAULICS. 123 

the squares of their areas, multiplied by their revolu- 
tions. 

8, If their diameters be equal, the quantity of surfaces 
passed, &c, are as their velocities or revolutions simply. 

But we have been supposing theory and practice to 
agree strictly, which they will by no means do in this 
case. To the quantity ground, and the proportion of 
power used by large stones more than by small ones, the 
ratio assigned by the theory will not apply ; because the 
meal having to pass a greater distance through the stone, 
is operated upon oftener, which operation must be lighter, 
else it will be overdone ; large stones may, therefore, be 
made to grind equal quantities with small ones, and 
with equal power, and to do it with less pressure ; there- 
fore, the flour will be better.* See Art. 111. 

From these considerations, added to experiments, I con- 
clude, that the power required and quantity ground, will 
be nearly as the area of the stones, multiplied into the 
velocity of the mean circles, or, which is nearly the same, 
as the squares of their diameters. But if the velocities 
of their mean circles or circumferences be equal, then it 
will be as their areas simply. 

On these principles I have calculated the following 
table, showing the power required, and quantity ground, 
both by theory, and, what I suppose to be, the most cor- 
rect practice. 

* A French author (M. Fahre) says that he has found hy experiments, that to 
produce the best flour, a stone 5 feet diameter should revolve between 48 and 61 
times in a minute. This is much slower than the practice in America, but we may 
conclude that it is best to err on the side of a slower than of a faster motion lhan 
that of common practice; especially when the power is too small for the size of the 
stone. 



124 



HYDRAULICS. 



[CHAP. III. 



A TABLE 

OF THE AREA OF MILLSTONES 

OF 
DIFFERENT DIAMETERS, 

And of the power required to move them with a mean velocity of IS feet per 

second, &c. 



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feet. 


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cuhs. 


feet. 




sup. ft. 


lbs. 


cuhs. 


lbs. 


lbs. 


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8.62 


51.72 


7.777 


138.8 


10312 


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2.3 


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11.56 


63.36 


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4.05 


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18.63 


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111.78 


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22.76 


136.5 














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24.96 


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27.27 


163.6 


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8.6 


192 


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29.67 


178. 














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6.5 


32.18 


196. 














8.4 


6.75 


34.77 


208.6 














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7. 


37.48 


225. 


15.55 


69.4 


97499 


14.06 


313 


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9.8 


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2 


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4 


5 


6 


7 


8 


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10 



Note. One foot is deducted for the eye in each stone, and the reason why, in 
the 7th column, the quantity ground is not exactly as the cubes of the diameter of 
the stones, and, in the 9th column, not exactly as the squares of its diameter, is 
the deduction for the eye, which being equal in each stone, destroys the proportion. 

The engine of a paper-mill, roll 2 feet diameter, 2 feet long, revolving 160 times 
in a minute, requires equal power with a 4 feet stone, grinding 5 bushels an hour. 



CHAP. III.] HYDRAULICS. 125 

I have now laid down, in Art 61, 02, and 63, a the- 
ory for measuring the power of any mill-seat, and for as- 
certaining the quantity of that power that mill-stones of 
different diameters will require, by which we can find 
the diameter of the stones to suit the power of the seat; 
and have fixed on six cubochs of that power per second 
to every superficial foot of the mill-stone, as requisite to 
move the mean circle»of the stone 18 feet per second, 
when in the act of grinding with moderate and sufficient 
feed ; and have allowed the passing of 34804 feet per mi- 
nute to grind 5 lbs. in the same time, which is the effect 
of the five feet stone in the table, by which, if right, we 
can calculate the quantity that a stone of any other size 
will grind with any given velocity. 

I have chosen a velocity of 18 feet per second for the 
mean circle of all stones, which is slower than the com- 
mon practice ; but not too slow for making good flour. 
See Art. 111. Here will appear the advantage of large 
stones over small ones ; for if we will mak^ small stones 
grind as fast as large ones, we must give them such ve- 
ocity as to heat the meal. 

But I must here inform the reader, that the experiments 
from which I have deduced the quantity of power to 
each superficial foot to be six cubochs, have not been 
sufficiently exact to be relied on; but it will be easy for 
every intelligent mill-wright to make accurate experi- 
ments to satisfy himself as to this point.* 



* After having published the first edition of this work, I have been informed 
that, by accurate experiments made at the expense of the British government, it 
was ascertained that the power produced by 40,000 cubic feet of water descend- 
ing 1 foot, will grind and bolt 1 bushel of wheat. If this be true, then to find the 
quantity that any stream will grind per hour, multiply the cubic feet of water that 
it affords per hour, by the virtual descent, (that is, half of the head above the 
wheel, added to the fall after it enters an overshot-wheel,) and divide that pro- 
duct by 40,000, and the quotient will be the answer in bushels per hour that the 
stream will grind. 



EXAMPLE. 

Suppose a stream afford 32,000 cubic feet of wafer per hour, and the total fall 
19,28 feet; then, by the table for over-shot mills, Art. 73, the wheel should be 16 
feet diameter, head above the wheel 3,28 feet. Then half 3,28 = 1,64, which 
added to 16 = 17,64 feet virtual descent, and 17,64 x 32000 = 563480, which 
divided by 40,000, gives 14,08 bushels per hour the str3am will grind. 



126 HYDRAULICS. [CHAP. III. 



ARTICLE 64. 
OF CANAL FOR CONVEYING WATER TO MILLS. 

In digging canals, we must consider that water will 
come to a level on its surface, whatever may be the 
form of the bottom. If we have once determined on 
the area of the section of the canal necessary to convey 
a sufficient quantity of water to the mill, we need only 
to keep to that area in the whole distance, without 
paying much regard to the depth or width, if there be 
rocks in the way. Much expense may be oftentimes 
saved, by making the canal deep where it cannot easily 
be made wide enough, and wide where it cannot easily 
be made sufficiently deep. Thus suppose we had de- 
termined it to be 4 feet deep, and 6 feet wide, then the 
area of its section will be 24. — Let fig. 36, Plate IV. 
represent a canal, the line A B the level or surface of 
the water, C D the side, E F the bottom, A C the width, 
6 feet, A E the depth, 4 feet. Then, if there be rocks 
at G, so that we cannot, without great expense, obtain 
more than 3 feet width, but can go 8 feet deep at a small 
expense : then 8x3 = 24, the section required. Again, 
suppose a flat rock to be at H, so that we cannot, with- 
out great expense, obtain more than 2 feet depth, but 
can, with small expense, obtain 12 feet width: then 2 x 
12 = 24, the section required; and the water will come 
on equally well even if it were not more than ,5 of a 
foot deep, provided it be proportionably wide. One dis- 
advantage, however, arises in having canals very shal- 
low in some places, because the water in dry seasons 
may be too low to rise over them; but if the water were 
always to be of one height, the disadvantage would be 
but trifling. The current will keep the deep places open, 
light sand or mud will not settle in them. This will seem 
paradoxical to some, but the experiment has been tried, 
and the fact established. 



CHAP. III.] HYDRAULICS. 127 

ARTICLE 65. 

OP THE SIZE AND FALL OF CANALS. 

As to the size and fall necessary to convey any quan- 
tity of water required to a mill, I do not find any rule 
laid down for either. But in order to establish one, 
let us consider, that the size depends entirely upon the 
quantity of water and the velocity with which it is to 
pass : therefore, if we can determine on the velocit}', 
which I will suppose to be from 1 to 2 feet per second 
— but the slower the better, as there will be the less 
fall lost — we can find the size of the canal by the follow- 
ing 

THEOREM. 

Divide the quantity required in cubic feet per se- 
cond by the velocity in feet per second, and the quo- 
tient will be the area of the section of the canal. Divide 
that area by the proposed depth, and the quotient is the 
width : or, divide by the width, and the quotient is the 
depth. 

PROBLEM. 

Given, a 5 feet mill-stone, its mean circle to be moved 
with a velocity of 18 feet per second, on a seat of 10 feet 
virtual, or effective, descent, required the size of the ca- 
nal, with a velocity of 1 foot per second. 

Then, by theorem in Art. 63 : the area of the stone 
18,63 feet multiplied by 6 cubochs of power, is equal 
111,78 cubochs for the power (in common practice, say 
112 cubochs) which divided by 10, the fall, quotes 11,178 
cubic feet required per second, which divided by l,the 
velocity proposed per second, gives 11,178 feet, the area 
of the section, which divided by the depth proposed, 2 
feet, gives 5,58 feet for the width. 



128 HYDRAULICS. [CHAP. III. 



PROBLEM II. 

Given, a mill-stone 6 feet diameter, to be moved with 
a velocity of 18 feet per second of its mean circle, to be 
turned by an undershot-wheel on a seat of 8 feet per- 
pendicular descent, required the power necessary per 
second to drive them, and the quantity of water per se- 
cond to produce said power, likewise the size of the ca- 
nal to convey the water with a velocity of 1,5 feet per 
second. 

Then, by Art. 61, 8 feet perpendicular descent, on 
the undershot principle, is only = 4 feet virtual or effec- 
tive descent : and the area of the stone b}^ the table (Art. 
63) = 27,27 feet x 6 cubochs = 163,62 cubochs for the 
power per second, which divided by 4, the effective 
descent = 40,9 cubic feet, the quantity required per se- 
cond, which divided by the velocity proposed, 1,5 feet 
per second = 27,26, for the area of the section of the ca- 
nal, which divided by 2,25 feet, the depth of the canal 
proposed = 12 feet the width.* 

As to the fall necessary in the canal, I may observe, 
that the fall should be in the bottom of the canal, and 
none on the top, which should be all the way on a level 
with the water in the dam, in order that when the gate 
is shut down at the mill, the water may not overflow 
the banks, but stand at a level with the water in the 
dam ; that is, as much fall as there is to be in the whole 
length of the canal, so much deeper must the canal be 
at the mill than at the dam. From many observations 
I conclude that about 3 inches to 100 yards will be suffi- 
cient, if the canal be long, but more will be requisite 
if it be short, and the head apt to run down when 
water is scarce, for the shallower the water, the great- 
er must be the velocity, and the more fall is required. 
- — A French author, M. Fabre, allows one inch to 500 
feet. 

* An acre of a mill-pond contains 43560 cubic feet of water, for every foot of 
its depth. 

Suppose your pond contain 3 acres, and is 3 feet deep, then 43560, multiplied 
by 3, is equal 130680, which multiplied by 3, is equal 392040 cubic feet, its con-. 
tents, which divided by the cubic feet your mill uses per second (say 10,) is equal 
39'204 seconds, or 10 hours, the time the pond will keep the mill going. 



CHAP. HI.] HYDRAULICS. 129 

ARTICLE 66. 

OF AIR-PIPES TO PREVENT TIGHT TRUNKS FROM BURSTING WHEN 
FILLED WITH WATER. 

When water is to be conveyed under ground or in a 
tight trunk below the surface of the water in the reser- 
voir, to any considerable distance, there must be air- 
pipes (as they have been called) to prevent the trunk 
from bursting. To understand their use, let us suppose 
a trunk 100 feet long, and 16 feet below the surface of the 
water; to fill which, a gate is to be drawn at one end, of 
equal size with the trunk. Then, if the water meet no 
resistance in passing to the other end, it acquires great 
velocity, which is suddenly to be stopped when the trunk 
is full. This great column of water, in motion, in this 
case, w r ould strike with a force equal to that of a solid 
body of equal weight and velocity, the shock of which 
would be sufficient to break any trunk that ever was made 
of wood. Many having thought the use of these pipes to 
be to let out the air, have made them too small ; so that 
they would vent the air fast enough to let the water in 
with considerable velocity, but would not admit the wa- 
ter fast enough to check its motion gradually; in which 
case they are worse than useless ; for if the air cannot 
escape freely, the water cannot enter freely, and the 
shock will be decreased by its resistance. 

Whenever the air has been compressed in the trunk 
by the water coming in, it has made a great blowing 
noise in escaping through the crevices, and, therefore, 
has been viewed as the cause of the bursting of the trunk ; 
whereas it acted by its elastic principle, as a great pre- 
ventive against it. For, I apprehend, that if we were 
to pump all the air out of a trunk, 100 feet long, and 3 
by 3 feet wide, and to let the water in with full force, 
it would burst were it as strong as a cannon of cast me- 
tal; because, in that case, there would be 900 cubic feet 
of water, equal to 56250 lbs. pressed on by the weight of 
the atmosphere, with a velocity of 47 feet per second, to 
be suddenly stopped, the shock of which would be al- 
most irresistible. 
9 



130 HYDRAULICS. [CHAP. III. 

I consider it best, therefore, to make an air-pipe of the 
full size of the trunk, every 20 or 30 feet ; but this will 
depend much on the depth of the trunk below the sur- 
face of the reservoir, and upon other circumstances. 

Having now said what was necessary, in order the bet- 
ter to understand the theory of the power an4 principles 
of mechanical engines, and of water acting on water- 
wheels upon different principles, and, for establishing 
true theories of the motion of the different kinds of wa- 
ter-wheels, I here quote many of the celebrated Mr. 
Smeaton's experiments, that the reader may compare 
them with the theories proposed, and judge for himself. 



article 67. 

smeaton's experiments. 

" An experimental Inquiry, read in the Philosophical Society 
in London, May 3c?, and 10th, 1759, concerning the Na- 
tural Powers of Water to turn Mills and other machines, 
depending on a circular Motion, by James Sm'eaton, 
F. R. S. 

" What I have to communicate on this subject was 
originally deduced from experiments made on working 
models, which I look upon as the best means of obtaining 
the outlines in mechanical inquiries. But in this case it 
is necessary to distinguish the circumstances in which 
a model differs from a machine in large; otherwise a mo- 
del is more apt to lead us from the truth than towards it. 
Hence the common observation, that a thing may do very 
well in a model that will not do in large. And, indeed, 
though the utmost circumspection be used in this way, 
the best structure of machines cannot be fully ascertained, 
but by making trials with them of their proper size. It 
is for this purpose that, though the models referred to, 
and the greatest part of the following experiments, were 
made in the years 1752 and 1753, yet I deferred offering 
them to the society till I had an opportunity of putting 



CHAP. III.] HYDRAULICS. 131 

the deductions made therefrom in real practice, in a va- 
riety of cases and for various purposes ; so as to be able 
to assure the society that I have found them to answer.*' 



PART I. 

CONCERNING UNDERSHOT WATER WHEELS. 

" Plate XII. is a view of the machine for experiments 
on water wheels, wherein 

ABCD is the lower cistern or magazine for receiving 
the water after it has left the wheel, and for supplying 

DE, the upper cistern or head, wherein the water be- 
ing raised to any height by a pump, that height is shown 

FG, a small rod divided into inches and parts, with a 
float at the bottom to move the rod up and down, as the 
surface of the water rises and falls. 

HI is a rod by which the sluice is drawn, and stopped 
at any height required by means of 

K, a pin or peg, which fits several holes placed in the 
manner of a diagonal scale upon the face of the rod 
HI. 

GL is the upper part of the rod of the pump for draw- 
ing the water out of the lower cistern, in order to raise 
and keep up the surface thereof to its desired height in 
the head DE, thereby to supply the water expended by 
the aperture of the sluice. 

MM is the arch and handle of the pump, which is 
limited in its stroke by 

N, a piece for stopping the handle from raising the 
piston too high, that also being prevented from going too 
low, by meeting the bottom of the barrel. 

O is a cylinder upon which the cord winds, and which 
being conducted over the pulleys P and Q, raises 

R, the scale into which the weights are put for trying 
the power of the water. 

W the beam which supports the scale that is placed 
15 or 16 feet higher than the wheel. 



132 HYDRAULICS. [CHAP. III. 

XX is the pump-barrel, 5 inches diameter and 11 inches 
long. Y is the piston, and Z is the fixed valve. 

GV is a cylinder of wood, fixed upon the pump-rod, and 
reaches above the surface of the water; this piece of wood 
being of such thickness that its section is half the area 
of the pump-barrel, will cause the water to rise in the 
head as much while the piston is descending as while it 
is rising, and will thereby keep the gauge-rod F G more 
equally to its height. 

a a shows one of the two wires that serve as a director 
to the float, b is the aperture of the sluice, c a is a 
cant-board for canting the water down the opening c d 
into the lower cistern. c e is a sloping board for 
bringing back the water that is thrown up by the 
wheel. 

There is a contrivance for engaging and disengaging 
the scale and weight instantaneously from the wheel, 
by means of a hollow cylinder on which the cord winds 
by slipping it on the shaft; and when it is disengaged, 
it is held to its place by a ratchet-wheel: for without 
this, experiments could not be made with any degree of 
exactness. 

The apparatus being now explained, I think it ne- 
cessary to assign the sense in which I use the term 
power. 

The word power is used in practical mechanics, I ap- 
prehend, to signify the exertion of strength, gravity, im- 
pulse, or pressure, so as to produce motion. 

The raising of a weight, relative to the height to 
which it can be raised in a given time, is the most pro- 
per measure of power. Or, in other words, if the weight 
raised be multiplied by the height to which it can be 
raised in a given time, the product is the measure of the 
power raising it; and, consequently, all those powers are 
equal. But note, all this is to be understood in case of 
slow or equable motion of the body raised ; for in quick, 
accelerated or retarded motions, the vis inertia of the 
matter moved will make a variation. 

In comparing the effects produced by water wheels 
with the powers producing them ; or, in other words, to 



CHAP. III.] HYDRAULICS. 133 

know what part of the original power is necessarily lost 
in the application, we must previously know how much 
of the power is spent in overcoming the friction of the 
machinery and the resistance of the air; also what is the 
real velocity of the water at the instant it strikes the 
wheel, and the real quantity of water expended in a 
given time. 

From the velocity of the water at the instant that it 
strikes the wheel, given ; the height of the head pro- 
ductive of such velocity can be deduced, from acknow- 
ledged and experienced principles of hydrostatics : so 
that by multiplying the quantity or weight of water 
really expended in a given time, by the height of head 
so obtained, which must be considered as the height from 
which that weight of water had descended, in that given 
time, we shall have a product equal to the original pow- 
er of the water, and clear of all uncertainty that would 
arise from the friction of the water in passing small 
apertures, and from all doubts, arising from the differ- 
ent measure of spouting waters, assigned by different 
authors. 

On the other hand, the sum of the weight raised by the 
action of this water, and of the weight required to over- 
come the friction and resistance of the machine, multi- 
plied by the height to which the weight can be raised in 
the given time, the product will be the effect of that pow- 
er; and the proportion of the two products will be the 
proportion of the power to the effect: so that by loading 
the wheel with different weights successively, we shall 
be able to determine at what particular load and velocity 
of the wheel the effect is a maximum. 



To determine the Velocity of the Water striking the Wheel. 

" First, let the wheel be put in motion by the water, 
but without any weight in the scale ; and let the number 
of turns in a minute be 60 : now, it is evident, that were 
the wheel free from friction and resistance, that 60 times 
the circumference of the wheel would be the space 
through which the water would have passed in a minute 



134 HYDRAULICS. [CHAP. III. 

with that velocity wherewith it struck the wheel. But 
the wheel being encumbered with friction and resist- 
ance, and yet moving 60 turns in a minute, it is plain, 
that the velocity of the water must have been greater 
than GO circumferences, before it met with the wheel. 
Let the cord now be wound round the cylinder, but con- 
trary to the usual way, and put as much weight in the 
scale as will, without any water, turn the wheel somewhat 
faster than 60 turns in a minute, suppose 63, and call this 
the counter-weight; then let it be tried again with the 
water assisted by this counter-weight, the wheel, there- 
fore, will now make more than 60 turns in a minute, sup- 
pose 64, hence we conclude the water still exerts some 
power to turn the wheel. Let the weight be increased 
so as to make 64 § turns in a minute without the water, 
then try it with the water and the weight as before, and 
suppose it now make the same number of turns with the 
water, as without; namely, 64|, hence, it is evident, that 
in this case the wheel makes the same number of turns 
as it would with the water, if the wheel had no friction 
or resistance at all, because the weight is equivalent 
thereto ; for if the counter-weight were too little to over- 
come the friction, the water would accelerate the wheel, 
and if too great it would retard it: for the water in this 
case becomes a regulator of the wheel's motion, and the 
velocity of its circumference becomes a measure of the 
velocity of the water. 

In like manner, in seeking the greatest product or max- 
imum of effect; having found by trials what weight gives 
the greatest product, by simply multiplying the weight 
in the scale by the number of turns of the wheel, find 
what weight in the scale, when the cord is on the con- 
trary side of the cylinder, will cause the wheel to make 
the same number of turns, the same way, without water: 
it is evident that this weight will be nearly equal to all 
friction and resistance taken together; and, consequent- 
ly, that the weight in the scale, with twice* the weight 
of the scale, added to the back or counter-weight, will 

* The weight of the scale makes part of the weight both ways, namely ; both 
of the weight and counter-weight. 



CHAP. III.] HYDRAULICS. 135 

be equal to the weight that could have been raised, sup- 
posing the machine had been without friction or resist- 
ance, and which multiplied by the height to which it 
was raised, the product will be the greatest effect of that 
power. 

The quantity of Water expended is found thus : — 

" The pump was so carefully made, that no water 
escaped back through the leathers, it delivered the same 
quantity each stroke, whether quick or slow, and by as- 
certaining the quantity of 12 strokes and counting the 
number of strokes in a minute that was sufficient to keep 
the surface of the water to the same height, the quan- 
tity expended was found. 

These things will be farther illustrated by going over 
the calculations of one set of experiments. 

Specimen of a Set of Experiments. 

The sluice drawn to the first hole. 
The water above the floor of the sluice, 30 inches. 
Strokes of the pump in a minute, 39| 

The head raised by 12 strokes, 21 

The wheel raised the empty scale and made > ~~ 

turns in a minute, \ 

With a counter-weight of one lb. 8 oz. it) «- 

made, ) 

Ditto, tried with water, 86 

No. 
1 
2 
3 
4 
5 
6 
7 



* When the wheel moves so slowly as not to rid the water as fast as supplied 
by the sluice, the accumulated water falls back upon the aperture, and the wheel 
immediately ceases moving. 

Note. This note of the author argues in favour of drawing the gate near the 
float. 



lbs. oz. 


turns 


in a min. 




product. 


4:0 




45 




180 


5:0 




42 




210 


6:0 




36} 




217* 


7:0 




33| 




236} 


8:0 




30 




240 max 


9 :0 




261 




238. V 


10:0 




22 




220" 


11 :0 




164 




181£ 


12:0 




* ceased 


workin 


a* 



136 HYDRAULICS. [CHAP. III. 

Counter-weight for 30 turns without water 2 oz. in the 
scale. 

N. B. The area of the head was 105,8 square inches, 
weight of the empty scale and pulley 10 ounces, circum- 
ference of the cylinder 9 inches, and circumference of 
the water-wheel 75 inches. 



Reduction of the above Set of Experiments. 

The circumference of the wheel 75 inches, multi- 
plied by 86 turns, gives 6450 inches for the velocity of 
the water in a minute, l-60th of which will be the velo- 
city in a second, equal to 107,58 inches, or 8-96 feet, 
which is due to a head of 1,5 inches,* and this we call 
the virtual or effective head. 

The area of the head being 105,8 inches, this multi- 
plied by the weight of water of one cubic inch, equal 
to the decimal of ,579 of the ounce avoirdupois, gives 
61,26 ounces for the weight of as much water as is con- 
tained in the head upon one inch in depth, l-10th of 
which is 3,83 lbs.; this multiplied by the depth 21 
inches, gives 80,43 lbs. for the value of 12 strokes, and 
by proportion 39| (the number made in a minute) will 
give 264,7 lbs., the weight of water expended in a 
minute. 

Now, as 264,7 lbs. of water may be considered as having 
descended through a space of 15 inches in a minute, the 
product of these two numbers 3970, will express the pow- 
er of the water to produce mechanical effect; which are 
as follows : — 

The velocity of the wheel at a maximum, as appears 
above, was 30 turns in a minute; which, multiplied by 9 
inches, the circumference of the cylinder, makes 270 
inches: but as the scale was hung by a pulley and dou- 
ble line, the weight was only raised half of this, namely; 
135 inches. 

* This is determined by the common maxim of hydrostatics; that the velocity 
of spouting water is equal to the velocity that a heavy body would acquire in 
falling from the height of the reservoir; and is proved by the rising of jets lo the 
height of their reservoirs nearly. 



CHAP. III.] HYDRAULICS. 137 

lbs. oz. 







The weight in the scale at the ) ft 

maximum, £ 

Weight of the scale and pul- ) ^ , ~ 

Counter-weight, scale, and pul- ) ^ , ^ 

le y» 3 



Sum of the resistance, lbs. 9 6, or 9,375 lbs. 

Now, as 9,375 lbs. are raised 135 inches, these two 
numbers being multiplied together produce 1266, which 
expresses the effect produced at a maximum: so that the 
proportion of the power to the effect is as 3970 : 1266, or 
as 10: 3,18. 

But though this be the greatest single effect produci- 
ble from the power mentioned, by the impulse of the wa- 
ter upon an undershot wheel ; yet, as the whole power of 
the water is not exhausted thereby, this will not be the 
true ratio between the power and the sum of all the ef- 
fects producible therefrom: for, as the water must ne- 
cessarily leave the wheel with a velocity equal to the 
circumference, it is plain that some part of the power of 
the water must remain after leaving the wheel. 

The velocity of the wheel at a maximum is 30 turns a 
minute, and, consequently, its circumference moves at 
the rate of 3,123 feet per second, which answers to a 
head of 1,82 inches; this being multiplied by the ex- 
pense of water in a minute: namely, 264,7 lbs., produces 
481 for the power remaining: this being deducted from 
the original power, 3970, leaves 3489, which is that part 
of the power that is spent in producing the effect 1266; 
so that the power spent, 3489, is to its greatest effect 
1266, as 10: 3,62, or as 11 : 4. 

The velocity of the water striking the wheel 86 turns 
in a minute, is to the velocity at a maximum 30 turns a 
minute, as 10: 3,5 or as 20 to 7, so that the velocity of 
the wheel is a little more than l-3d of the velocity of the 
water. 

The load at a maximum has been shown to be equal to 
9 lbs. 6 oz. and that the wheel ceased moving with 12 



138 HYDRAULICS. [CHAP. III. 

lbs. in the scale ; to which, if the weight of the scale be 
added, namely; 10 oz.,* the proportion will be nearly as 3 
to 4, between the load at a maximum and that by which 
the wheel is stopped.t 

It is somewhat remarkable, that, though the velocity 
of the wheel in relation to the water turns out greater 
than l-3d of the velocity of the water, yet the impulse 
of the water in case of the maximum is more than dou- 
ble of what is assigned by theory; that is, instead of 
4-9ths of the column, it is nearly equal to the whole co- 
lumn 4 

It must be remembered, therefore, that in the present 
case, the wheel was not placed in an open river, where 
the natural current, after it has communicated its im- 
pulse to the float, has room on all sides to escape as the 
theory supposes ; but in a conduit or race, to which the 
float being adapted, the water cannot otherwise escape 
than by moving along with the wheel. It is observable, 
that a wheel working in this manner, as soon as the wa- 
ter meets the float, it, receiving a sudden check, rises 
up against the float, like a wave against a fixed object, 
insomuch, that when the sheet of water is not a quarter 
of an inch thick before it meets the float, yet this sheet 
will act upon the whole surface of a float, whose height 
is three inches; consequently, were the float no higher 
than the thickness of the sheet of water, as the theory 
also supposes, a great part of the force would be lost by 
the water dashing over it. 

* The resistance of the air in this case ceases, and the friction is not added, as 
12 lbs. in the scale was sufficient to stop the wheel after it had been in full mo- 
tion, and, therefore, somewhat more than a counterbalance for the impulse of the 
water. 

f I may here observe, that it is probable, that if the gate of the sluice had been 
drawn as near the float-boards as possible, [as is the practice in America, where 
water is applied to act by impulse alone,] that the wheel would have continued 
to move until loaded with 1§ times the weight of the maximum load; namely, 9 
lbs. 6 oz. multiplied by H, equal to 14 lbs. 1 oz. It would then have agreed 
with the theory established Art. 41. This, perhaps, escaped the notice of our au- 
thor. 

t This observation of the author I think a strong confirmation of the truths of 
the theory established Art. 41, where the maximum velocity is made to be ,577 
parts of the velocity of the water, and the load to be 2-3ds the greatest load: for 
if the gate had been drawn near the floats, the greatest load would probably have 
been 14 lbs. 1 oz. or as 3 to 2 of the maximum load. 



CHAP. III.] HYDRAULICS. 139 

In confirmation of what is already delivered, I have 
subjoined the following table, containing the result of 
27 experiments made and reduced in the manner above 
specified. What remains of the theory of undershot 
wheels, will naturally follow from a comparison of the 
different experiments together. 



140 



HYDRAULICS. 

A TABLE OF EXPERIMENTS. 

NO. 1. 



[chap. III. 








1 






















W 


W 






8, 






















p 


p 






era 1 L? 

IT 3 


< 


H 




o 


t" 1 




3 

p 






p 
5" 


o 
o 

"a 


o 

CD 




3 

s 

3 


CD 

p 

to 


o 

3- 

CD 

i 

TO 


CD 
P 
P. 
& 
CD 
p. 

d 

o 


a 

a 

00 
P 

P 

3 


V 


S3 

CD 
CD 

n 


p 
p. 

p 
t? 

CD 

3 




CD 
-i 

CD 
X 

ts 

CD 
P 

P- 
CD 

a. 


o 

CD 


o 


o 

CD 
O 
CD 


3* 

CD 

<i 

CD 

§-2. 

CD >-* 

£L cd" 


p-— 

^§ 
p- 


X 

-3 

o 

-i 

3 

CD 


hi 


5' 




CD 
P. 


x 






x 




3 






1-1 


O 


BcT 


3 




CD 

b 
t» 

re 

-; 
3 


3_ 

5T 

P 

P. 
CD 


P" 1 
CD 
*i 
CD 

O 

3 


3 
q 

3 




>-> 

3" 
3 


3 
p 
3 




p 
3. 
5 
p 

CD 






s 
Pi 

CD 

a? 

CD 
O 


r+ 
3" 
CD 

si 

p 

CD 

<-* 

P 

3 
p. 


— ■ CD 
1 = 

?| 

B' 

3 

o 




1 


in. 
33 




inch. 




lb. 


oz. 


lb. oz. 


lbs. 














88 


15.85 


30 


13 


10 


10 


9 


275 


4358 


1411 


10:3.24'l0:3.4 


10:7.75 




2 


30 


86 


15. 


30 


12 


10 


9 


6 


264. 7 


3970 


1266 


10:3.2 1!:3.5 


10:7.4 


^r> 


3 


27 


82 


13.7 


28 


11 


2 


8 


6 


243 


3329 


1044 


10:3.1510:3.4 


10:7.5 




4 


24 


78 


12.3 


27.7 


9 


10 


7 


5 


235 


2890 


901.4 


10:3.1210:3.55 


10:7.53 


br 


5 


2175 


11.4 


25.9 


8 


10 


6 


5 


214 


2439 


735.7 


10:3.02,10:3.45 


10:7.32 


ib 


G 


18 70 


9.95 


23.5 


6 


10 


5 


5 


199 


1970 


561.8 


10:2.85 10:3.36 


10:8.02 


Tr 


? 


15 65 


8.54 


23.4 


5 


2 


4 


4 


178.5 


1524 


442.5 


10:2.9 


10:3.6 


10:8.3 


£ 


8 


iatio 


7.29 


22 


3 


10 


3 


5 


161 


1173 


328 


10:2.8 


10:3.77 


10:9.1 


O 


.9 


9 52 


5.47 


19 


2 


12 


2 


8 


134 


733 


213.7 


10:2.9 


10:3.65 


10:9.1 


TO 


10 


642 


3.55 


16 


1 


1^ 


1 


10 


114 


404.7 


117 


10:2.8210:3.8 


10:9.3 




11 


24 84 


14.2 


30. 75 


13 


10 


10 


14 


342 


4890 


1505 


10:3.0710:3.6610:7.9 |> 


12 


2181 


13.5 


29 


11 


10 


9 


6 


297 


4009 


1223 


10:3.01 10:3t62 10:8.05 ^ 


13 


18 72 


10.5 


26 


9 


10 


8 


7 


285 


2993 


975 


10:3.3510:3.6 10:8.75 =f 


14 


15 69 


9.6 


25 


7 


10 


6 


14 


277 


2659 


774 


10:2.9210:3.6210:9. 


TO 


if, 


12 63 


8.0 


25 


5 


10 


4 


14 


234 


1872 


549 


10:2.9410:3.97 10:8.7 


TO 


1G 


9 56 


6.37 


23 


4 





3 


13 


201 


1280 


390 


10:3.0510:4.1 


10:9.5 


3 


17 

18 


6 46 
15 72 


4.25 


21 


2 


8 


2 


4 


167.5 


712 


212 


10:2.98 


10:4.55 


10:9. 




10.5 


29 


11 


10 


9 


G 


357 


3748 


1201 


10:3.23 


10:4.02 


10:8.05 




1!) 


12 66 


8.75 


26.75 


8 


10 


7 


6 


330 


2887 


878 


10:3.05 


10:4.05 


10:8.1 


W 


■20 


9,58 


6.8 


24.5 


5 


8 


5 





255 


1734 


541 


10:1.01 


10:4.22 


10:9.1 


7~ 


•21 


6 48 


4.7 


23.5 


3 


2 


3 





228 


1064 


317 


10:2.99 


10:4.9 


10:9.6 


. 


2'2 


1268 


9.3 


27 


9 


2 


8 


6 


359 


3338 


1006 


10:3.02 


10:3.97 


10:9.17 




23 


9,58 


6.8 


26. 25 


6 


2 


5 


13 


332 


2257 


686 


10:3.04 


10:4.52 


10:9.5 




24 


6 48 


4.7 


24.5 


3 


12 


3 


8 


262 


1231 


385 


10:3.13 


10:5.1 


10:9.35 




25 


9,60 


7.29 


27.3 


6 


12 


6 


6 


355 


2588 


783 


10:3.03 


10:4.55 


10:9.45 


ai 


2G 


6 50 


5.03 


24.6 


4 


6 


4 


1 


307 


1544 


456 


10:2.92 


10:4.9 


10:9.3 


p- 


27 


650 


5.03 


26 


4 


15 


4 


9 


360 


1811 


534 


10:2.95 


10:5.2 


10:9.25 m 


1 


2l3 


4 


5 




6 


7 




8 


9 


10 


11 


12 


13 1 



CHAP. III.] HYDRAULICS. 141 

Maxims and Observations deduced from the foregoing 
Table of Experiments. 

Max. I. That the virtual or effective head being the 
same, the effect will be nearly as the quantity of water 
expended. 

This will appear by comparing the contents of the 
columns 4, 8, and 10, in the foregoing sets of experiments, 
as, for 

Example I. taken from No. 8 and 25; namclif: — 

No. Virtual head. Water expended. Effect. 

8 7,29 161 328 

25 7,29 355 785 

Now, the beads being equal, if the effects be propor- 
tioned to the water expended, we shall have by maxim 1, 
as 161 : 355 : : 328 : 723 ; but 723 falls short of 785, as 
it turns out in experiment, according to No. 25 by 62. 
The effect, therefore, of No. 25, compared with No. 8, is 
greater than, according to the present maxim, in the ratio 
of 14 to 13.* 

The foregoing example, with four similar ones, may 
be seen at one view in the following table. 

* If the true maximum velocity of the wheel be ,577 of the velocity of the water, 
and the true maximum load be 2-3ds of the whole column, as shown in Art. 4'J; 
then the effect will be to the power in the ratio of 100 to 38, or as 10 to 3,8, a little 
more than appears by the table of experiments in columns 9 and 10: the difference 
is owing to the disadvantageous application of the water on the wheel in the model. 



142 



HYDRAULICS. 



[chap. III. 



TABLE OF EXPERIMENTS. 
NO. II. 



Proportional 


CO 


CM 
CM 


CO 


t~ 




variation. 


^f 


CM 


CO 
CO 


GO 
—1 


GO 


Variation. 


CM 

co 

-f- 


i 


1 

00 


+ 
CM 


+ 

co 




CO 
CM 


cm 

CM 


o 


co 

CO 


CO 


O 

t/2 

>— l 

<! 

CM 

o 
o 


00 

CO 


05 


r-4 


CO 


o 


CO 


CO 


CM 
CO 

co 


CM 
CO 
CM 


o 

CO 
CO 


co 


lO 
GO 
CM 


CM 


GO 
CM 
CM 


o 

CO 


Effect. 


CO lO 
CM GO 
CO t~ 


lO o 
r 1 

C3 CM 


-H CO 

lO CO 


r- io 

^ GO 
CO CO 


o ^ 

m co 

T UO 


Expense of water. 


— Ifl 

co no 

—1 CO 


GO to 
CM CO 


lO CM 
HO CO 
CM co 


GO CM 
CM CO 
CM CM 


t~ o 

o co 

CO CO 


Virtual head. 


<T5 CT> 

e* cm 


o o 


00 GO 

CO CO 


t-- t— 


CO CO - 

o o 

i-O uO 


No. Table I. 


00 to 
CM 


CO CO 


r>> co 
CM CM 


■— i CM 
CM Tf 


CM CM 


Examples. 


43 


-6 

CM 


-a 

CO 







CHAP. III.] HYDRAULICS. 143 

By this table of experiments, it appears that some fall 
short of, and others exceed, the maximum, and all agree 
as nearly as can be expected in an affair where so many 
different circumstances are concerned ; therefore, we may 
conclude the maxim to be true. 

Max. II. That the expense of the water being the same, 
the effect will be nearly as the height of the virtual or 
effective head. 

This also will appear by comparing the contents of co- 
lumns 4, 8? and 10, in any of the sets of experiments. 



Example I. of No. 2 and No. 24. 



No. 


Virtual Head. 


Expense. 


Effect. 


2 


15 


264,7 


1266 


24 


4,7 


262 


85 



Now, as the expenses are not quite equal, we must 
proportion one of the effects accordingly, thus: — 
By maxim I. 262 : 264,7 :: 385 : 389 

And by max. II. 15 : 4,7 :: 1266 : 397 



Difference, 8 

The effect, therefore, of No. 24, compared with No. 
2, is less than according to the present maxim, in the ra- 
tio of 49 : 50. 

Max. III. That the quantity of water expended being 
the same, the effect is nearly as the square root of its ve- 
locity. 

This will appear by comparing the contents of co- 
lumns 3, 8, and 10, in any set of experiments; as for 

Example I. of No. 2. with No. 24 ; namely : — 



No. 


Turns in a minute. 


Expense. 


Effect. 


2 


86 


264,7 


1266 


24 


48 


262 


385 



The velocity being as the number of turns, we shall 
have, 



144 HYDRAULICS. [CKAP. III. 

By maxim I. 262 : 264,7 :: 285 : 389 

And by max. III. J 7396:2304 { 1266:394 

Difference, 5 

The effect of No. 24, compared with No. 2, is less than 
by the present maxim in the ratio of 78 : 79. 

Max. IV. The aperture being the same, the effect will 
be nearly as the cube of the velocity of the water. 

This also will appear by comparing the contents of co- 
lumns 3, 8, and 10, as for 

Example, No. 1, and No. 10; namely: — 



No. 


Turns. 


Expense. 


Effect. 


1 


88 


275 


1411 


L0 


42 


114 


111 



Lemma. It must here be observed, that, if water pass 
out of an aperture in the same section, but with different 
velocities, the expense will be proportional to the velocity ; 
and, therefore, conversely, if the expense be not propor- 
tional to the velocity, the section of water is not the same. 

Now, comparing the water discharged with the turns 
of Nos. 1 and 1 0, we shall have 88 : 42 : : 275 : 13 1 ,2 ; but the 
water discharged by No. 10 is only 114 lbs., therefore, 
thouo.h the sluice was drawn to the same height in No. 
10 as in No. 1, yet the section of the water passing out, 
was less in No. 10 than No. 1, in the proportion of 114 
to 131,2; consequently, had the effective aperture or sec- 
tion of the water been the same in No. 10 as in No. 1, so 
that 131,2 lbs. of water had been discharged instead of 
114 lbs. the effect would have been increased in the 
same proportion; that is, 



By lemma 88 

By maxim I. 1 14 

And by max. IV. j 6 |® 4?2 




:: 275:131,2 
:: 117:134,5 

: 1411:153,5 
Difference, 19 



CHAP. III.] HYDRAULICS. 145 

The effect, therefore, of No. 10, compared with No. 1, 
is less than ought to be, by the present maxim, in the 
ratio of 7 : 8. 

OBSERVATIONS. 

"Observ. 1st. On comparing columns 2 and 4, table 
I., it is evident that the virtual head bears no certain 
proportion to the head of water, but that when the aper- 
ture is greater, or the velocity of the water issuing there- 
from less, they approach nearer to a coincidence: and 
consequently, in the large opening of mills and sluices, 
where great quantities of water are discharged from mo- 
derate heads, the head of water and virtual head deter- 
mined from the velocity will nearer agree, as experience 
confirms. 

Observ. 2d. Upon comparing the several proportions 
between the powers and effects in column 11, the most 
general is that of 10 to 3, the extremes are 10 to 3,2 and 
10 to 2,8; but as it is observable, that where the quan- 
tity of water or the velocity thereof is great, that is, where 
the power is greatest, the 2d term of the ratio is greatest 
also, we may, therefore, well allow the proportion sub- 
sisting in large works as 3 to 1, 

Observ. 3d. The proportion of velocities between the 
water and wheel in column 12 is contained in the limits 
of 3 to 1 and 2 to 1 ; but as the greater velocities approach 
the limits' of 3 to 1, and the greater quantity of water 
approaches to that of 2 to 1, the best general proportion 
will be that of 5 to 2.* 

Observ. 4th. On comparing the numbers in column 
13, it appears, that there is no certain ratio between the 

* I will here observe, that Mr. Smeaton maybe mistaken in his conclusion, that 
the best general ratio of the velocity of the water to that of the wheel will be as 
5 to 2, because, we may observe, that, in the first experiment, where the virtual 
head was 15,85 inches, and the gate drawn to the first hole, the ratio is as 10 :3,4. 
But in the last experiment, where the head was 5,03 inches, and the gate drawn 
to the sixth hole, the ratio is as 10 : 5,2 : and that the 2d term of the ratio increases, 
gradually, as the head decreases, and quantity of water increases; therefore, we 
may conclude, that, in the large openings of mills, the ratio may approach 3 to 2, 
which will agree with the practice and experiments of many able mill- Wrights of 
America, and many experiments I have made on mills. And as it is better to give 
the wheel too great than too little velocity, I conclude, the wheel of an undershot 
mill must have nearly two-thirds of the velocity of the water to produce a maxi- 
mum effect. 

10 



146 HYDRAULICS. [CHAP. III. 

load that the wheel will carry at its maximum, and what 
will totally stop it; but that they are contained within the 
limits of 20 to 19 and of 20 to 15; but as the effect ap- 
proaches nearest to the ratio of 20 to 15 or of 4 to 3, when 
the power is greatest, whether by increase of velocity or 
quantity of water, this seems to be the most applicable 
to large works; but as the load that a wheel ought to 
have in order to work to the best advantage, can be as- 
signed by knowing the effect it ought to produce, and 
the velocity it ought to have in producing it, the exact 
knowledge of the greatest load that it will bear is of less 
consequence in practice.* 

It is to be noted, that in almost all of the examples 
under the last three maxims, (of the four preceding,) the 
effect of the less power falls short of its due proportion to 
the greater, when compared by its maxim. And hence, 
if the experiments be taken strictly, we must infer that 
the effects increase and diminish in a higher ratio than 
those maxims suppose; but as the deviations are not very 
considerable, the greatest being about 1-8 of the quan- 
tity in question, and as it is not easy to make experiments 
of so compound a nature with absolute precision, we may 
rather suppose that the less power is attended with some 
friction, or works under some disadvantage, not account- 
ed for: and, therefore, we may conclude, that these max- 
ims will hold very nearly, when applied to works in 
large. 

After the experiments above mentioned were tried, 
the wheel which had 24 floats was reduced to 12, which 
caused a diminution in the effect on account of a greater 
quantity of water escaping between the floats and the 
floor; but a circular sweep being adapted thereto, of 
such a length that one float entered the curve before the 
preceding one quitted it, the effect came so near to the 
former, as not to give hopes of increasing the effect by 
increasing the number of floats past 24 in this particular 
wheel. 

* Perhaps the author is here again deceived by the imperfection of the model, 
for had the water been drawn close to the float, the load that would totally stop the 
wheel would always be equal to the column of water, acting on the wheel. See 
the note, page 70. The friction of the shute and air destroyed great part of the 
force of his small quantity of water. 



CHAP. III.] HYDRAULICS. 147 



PART II. 

ARTICLE 68. 
CONCERNING OVERSHOT WHEELS. 

" In the former part of this essay, we have considered 
the impulse of a confined stream, acting on undershot 
wheels; we now proceed to examine the power and ap- 
plication of water, when acting by its gravity on overshot 
wheels. 

It will appear in the course of the following deduc- 
tions, that the effect of the gravity of descending bodies 
is very different from the effect of the stroke of such as 
are non-elastic, though generated by an equal mechanical 
power. 

The alterations of the machinery already described to 
accommodate the same for experiments on overshot 
wheels, were principally as follows: — 

Plate XII. The sluice I b being shut down, the rod 
H I was taken off. The undershot water-wheel was taken 
off the axis, and instead thereof, an overshot wheel of the 
same size and diameter was put in its place. Note, this 
wheel was 2 inches deep in the shroud or depth of the 
bucket, the number of buckets was 36. 

A trunk for bringing the water upon the wheel was 
fixed according to the dotted lines f g, the aperture was 
adjusted by a shuttle, which also closed up the outer end 
of the trunk, when the water was to be stopped. 



148 HYDRAULICS. [CHAP. III. 



Specimen of a set of Experiments. 

Head 6 inches — 14§ strokes of the pump in a minute, 12 
ditto = 80 lbs.* — weight of the scale (being wet) lOf 
ounces. 

Counter weight for 20 turns, besides the scale, 3 ounces. 



No. 


wt. in the scale. 


turns. 


product. 


Observations. 


1 





60 




threw most part of 


2 


1 


56 


the water out of the 


3 


2 


52 


wheel. 


4 


3 


49 


147) 


received the water 


5 


4 


47 


' 188$ 


more quietly. 


6 


5 


45 


225 




7 


6 


42 1 


255 




8 


7 


41 


287 




9 


8 


38| 


308 




10 


9 


36| 


328i 




li 


10 


35| 


355 




12 


11 


32| 


360| 




13^ 


12 


31| 


375 




14 ' 


13 


28| 


370| 




15 


14 


27 \ 


385 




16 


15 


26 


390 




17 


16 


24"i 


O %J **i 




18 


17 


22| 


3861 




19 


18 


21| 


391| 




20 


19 


201 


394| 
395 


) 


21 


20 


19| 


> maximum. 


22 


21 


18* 


383| 




23 


22 


18 


396 worked irregularly. 


24 


23 




overset by its load. 



* The small difference in the value of 12 strokes of the pump from the former 
experiments, was owing to a small difference in the length of the stroke, occa- 
sioned by the warping of the wood. 



CHAP. III.] HYDRAULICS. J 49 



Reduction of the preceding Specimen. 

" In these experiments the head being 6 inches, and the 
height of the wheel 24 inches, the whole descent will be 
30 inches; the expense of water was 14§ strokes of the 
pump in a minute, whereof 12 contained 80 lbs., there- 
fore, the water expended in a minute, was 96| lbs., which 
multiplied by 30 inches, give the power = 2900. 

If we take the 20th experiment for the maximum, we 
shall have 20| turns in a minute, each of which raised 
the weight 4| inches 9 that is, 93,37 inches in a minute. 
The weight in the scale was 19 lbs. the weight of the 
scale lOf oz., the counter- weight 3 oz. in the scale, which 
with the weight of the scale 10f oz., make in the whole 
20| lbs. which is the whole resistance or load; this, mul- 
tiplied by 93,37 makes 1914, for the effect. 

The ratio, therefore, of the power and effect will be as 
2900: 1914, or as 10:6,6, or as 3 to 2 nearly. 

But, if we compute the power from the height of the 
wheel only, we have 96| lbs. x 24 inches = 2320 for the 
power, and this will be to the effect as 2329 : 1914, or as 
10: 8,2, or as 5 to 4, nearly. 

The reduction of this specimen is set down in No. 9 
of the following table, and the rest were deduced from a 
similar set of experiments, reduced in the same manner. 



150 



HYDRAULICS. 



[CHAP. III. 



TABLE III. 



CONTAINING THE RESULT OF 16 SETS OF EXPERIMENTS ON 
OVERSHOT WHEELS. 





















W 










H 










W 


» 








i 


a 

a 

CO 


CD_ 


o 






p 
o" 


5" 

o 








p 


p 


ow" 


3 






o 


Hn 








Q 






CD 


Hd 




"a 
















•-I 


o 






a* 




3 

a 


4 


CD 

M 

CD 
3 


3 

P 


p_ 
c/T 

CD 


o 

CD 


3 

CD 
-i 

O 


H 


a* 

CD 

a" 


CD 

CD <; 

CD'S 
o ■ 


3 

CD 
P 


3 

CD 


p. 

cd 

CO 


P. 


3 


P 


* 

a* 


a 1 

CD 


a 


o 

CD 


3 
P 


-i 


o 


»T3 


a 


a' 


o_ 






T3 


' o 






CD 
3 


CD 

a 


3 


CD 

3 


cd* 
P. 


3 

a" 

CD 




O 
I 

CD 


a- 


?' 






CD 


p 


CD 


CD 




1-1 


CD 










>-i 


X 


QD 
















B' 






O 






P 










p 
? 


3 

B' 

a 

CD 


3 

a 

3 


CD 

3 






3 
O. 

CD 

a 


a" 

CD 
CD 

P 

a 






inches. 


lbs. 




lbs. 














1 


27 


30 


19 


6 1-2 


810 


720 


556 


10:6.9 


10:7,7 


CO CD 


2 


27 


56 2-3 


161-4 


14 1-2 


1530 


1360 


1060 


10:6.9 


10 :7.8 


3 


27 


562-3 


20 3-4 


12 1-2 


1530 


1360 


1167 


10:7.6 


10:8.4 


•• ^ 


4 


27 


631-3 


201-2 


13 1-2 


1710 


1524 


1245 


10:7.3 


10:8.2 


oo a 
-3 


5 


27 


762-3 


21 1-2 


15 1-2 


2070 


1840 


1500 


10:7.3 


10; 8.2 




6 


28 1-2 


731-3 


183-4 


17 1-2 


2090 


1764 


1476 


10:7 


10:8.4 


g 


7 
8 


28 1-2 


962-3 


201-4 


20 1-2 


2755 


2320 


1868 


10:6.8 


10:8.1 


to ** 


30 


90 


20 


19 1-2 


2700 


2160 


1755 


10:6.5 


10:8.1 


o 


9 


30 


962-3 


20 3-4 


20 1-2 


2900 


2320 


1914 


10:6.5 


10:8.2 




10 


30 


1 L3 1-3 


21 


23 1-2 


3400 


2720 


2221 


10:6.5 


10 : 8.2 


to 


I] 


33 


56 2-3 


201-4 


13 1-2 


1870 


1360 


1230 


10:6.6 


10:9. 


1— » 

o 


IS 


33 


136 2-3 


221-4 


21 1-2 


3520 


2560 


2153 


10:6.1 


10:8.4 




13 


33 


146 2-3 


23 


27 1-2 


4840 


3520 


2846 


10:5.9 


10:8.1 


w 


U 


35 


65 


19 3-4 


16 1-2 


2275 


1560 


1466 


10:6.5 


10:9.4 


o 


15 


35 


120 


211-2 


25 1-2 


4200 


2880 


2467 


10:5.9 


10:8.6 




IG 
1 


35 


163 1-2 


25 


26 1-2 


5728 


3924 


2981 


10:5.2 


10:7.6 


Cn 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 



CHAP. III.] HYDRAULICS. 151 



OBSERVATIONS AND DEDUCTIONS FROM THE FOREGOING EXPERI- 
MENTS. 

I. Concerning the Ratio between the Power and Effect of 

Overshot Wheels. 

"The effective power of the water must be reckoned 
upon the whole descent, because it must be raised to that 
height in order to be in a condition of producing the same 
effect a second time. 

The ratios between the power so estimated, and the 
effects at a maximum deduced from the several sets of 
experiments, are exhibited at one view in column 9 of 
table III.; and hence, it appears, that those ratios differ 
from that of 10 to 7,6 to that of 10 to 5,2; that is, nearly 
from 4:3 to 4:2. In those experiments where the 
heads of water and quantities expended are least, the pro- 
portion is nearly as 4 to 3 : but where the heads and quan- 
tities are greatest, it approaches nearer to that of 4 to 2, 
and by a medium of the whole the ratio is that of 3 : 2, 
nearly. We have seen before, in our observations upon 
the effects of undershot wheels, that the general ratio of 
the power to the effect, when greatest, was as 3 : 1. • The 
effect, therefore, of overshot wheels, under the same circum- 
stances of Quantity and fall, is, at a medium, double to that 
of the undershot: and a consequence thereof, that non-elastic 
bodies, when acting by their impulse or collision, communi- 
cate only a part of their original power: the other part 
being spent in changing their figure in consequence of the 
stroke.* 

The powers of water computed from the height of the 
wheel only, compared with the effects as in column 10, 
appear to observe a more constant ratio; for if we take 
the medium of each class, which is set down in column 

II, we shall find the extremes to differ no more than 
from the ratio of 10:8,1 to that of 20: 8,5 and as the se- 
cond term of the ratio gradually increases from 8,1 to 
8,5 by an increase of head from 3 inches to 11, the ex- 

* These observations of the author agree with the theory, Art. 41 — i~. I may 
add, that non-elastic bodies, when acting by impulse or collision, communicate only 
half of their original power, by the laws of motion. 



152 HYDRAULICS. [CHAP. III. 

cess of 8,5 above 8,1 is to be imputed to the superior im- 
pulse of the water at the head of 11 inches, above that 
of 3 inches ; so that if we reduce 8,1 to 8, on account of 
the impulse of the 3 inch head, we shall have the ratio 
of the power computed upon the height of the wheel 
only to the effect at a maximum, as 10:8, or as 5:4, 
nearly. And from the equality of the ratio, between 
power and effect, subsisting where the constructions are 
similar, we must infer that the effects as well as the pow- 
ers, are, as the quantities of water and perpendicular 
heights, multiplied together respectively. 



II. Concerning the most proper Height of the Wheel in 
proportion to the whole Descent. 

"We have already seen, in the preceding observation. 
that the effect of the same quantity of water, descend- 
ing through the same perpendicular space, is double, 
when acting by its gravity upon an overshot wheel, to 
what the same produces when acting by its impulse upon 
an undershot. It also appears, that, by increasing the 
heajd from 11 to 3 inches, that is, the whole descent, from 
27 to 35, or in the ratio of 7 to 9, nearly, the effect is 
advanced no more than in the ratio of 8,1 to 8,4; that is, 
as 7 : 7,26, and, consequently, the increase of the effect 
is not l-7th of the increase of the perpendicular height. 
Hence, it follows, that the higher the wheel is in propor- 
tion to the whole descent, the greater will be the effect ; 
because it depends less upon the impulse of the head, and 
more upon the gravity of the water in the buckets : and, 
if we consider how obliquely the water issuing from the 
head must strike the buckets, we shall not be at a loss to 
account for the little advantage that arises from the im- 
pulse thereof; and shall immediately see of how little con- 
sequence this impulse is to the effect of an overshot wheel. 
However, as every thing has its' limits, so has this: for 
thus much is desirable, that the water should have some- 
what greater velocity than the circumference of the 
wheel, in coming thereon; otherwise the wheel will not 
only be retarded by the buckets striking the water, but 



CHAP. III.] HYDRAULICS. 153 

thereby dashing a part of it over, so much of the power 
is lost. 

The velocity that the circumference of the wheel ought 
to have, being known, the head requisite to give the 
water its proper velocity is easily computed by the com- 
mon rules of hydrostatics, and it will be found much 
less than what is commonly practised. 

III. Concerning the velocity of the Circumference of the 
Wheel in order to produce the greatest effect. 

" If a body be let fall freely from the surface of the 
head to the bottom of the descent, it will take a certain 
time in falling, and in this case the whole action of gra- 
vity is spent in giving the body a certain velocity: but, 
if this body in falling be made to act upon some other 
body, so as to produce a mechanical effect, the falling 
body will be retarded; because a part of the action of 
gravity is then spent in producing the effect, and the re- 
mainder only giving motion to the falling body: and, 
therefore, the slower a body descends, the greater will 
be the portion of the action of gravity applicable to the 
producing of a mechanical effect. Hence we are led to 
this general rule, that the less the velocity of the wheel, 
the greater will be the effect thereof. A confirmation of 
this doctrine, together with the limits it is subject to in 
practice, may be deduced from the foregoing specimen 
of a set of experiments. 

From these experiments it appears, that when the 
wheel made about 20 turns in a minute, the effect was 
nearly upon the greatest; when it made 30 turns, the ef- 
fect was diminished about l-20th part; but that, when it 
made 40, it was diminished about l-4th: when it made 
less than ISf, its motion was irregular; and when it was 
loaded so as not to admit its making 18 turns, the wheel 
was overpow r ered by its load. 

It is an advantage in practice, that the velocity of the 
wheel should not be diminished farther than what will 
procure some solid advantage in point of power; because, 
as the motion is slower, the buckets must be n; \de larger, 



154 HYDRAULICS. [CHAP. III. 

and the wheel being more loaded with water, the stress 
upon every part of the work will be increased in propor- 
tion: the best velocity for practice, therefore, will be 
such as when the wheel here used made about 30 turns 
in a minute; that is, when the velocity of the circumfe- 
rence is a little more than 3 feet in a second. 

Experience confirms, that this velocity of 3 feet in a 
second is applicable to the highest overshot wheels as 
well as the lowest; and all other parts of the work being 
properly adapted thereto, will produce very nearly the 
greatest effect possible. However, this also is certain, 
from experience, that high wheels may deviate farther 
from this rule, before they will lose their power, by a 
given aliquot part of the whole, than low ones can be ad- 
mitted to do: for a wheel df 24 feet high may move at 
the rate of 6 feet per second without losing any consi- 
derable part of its power: and, on the other hand, I have 
seen a wheel of 33 feet high that has moved very stea- 
dily and well, with a velocity but little exceeding 2 
feet."* 

[Mr. Smeaton has also made a model of a wind-mill, 
and a complete set of experiments on the power and ef- 
fect of the wind, acting on wind-mill sails of different 
constructions. But as the accounts thereof are quite too 
long for the compass of my work, I, therefore, extract 
little more than a few of the principal maxims deduced 
from his experiments, which, I think, may not only be of 
use to those who are concerned in building wind-mills, 
but may, also, serve to confirm some principles deduced 
from his experiments on water-mills.] 

* Probably this wheel was working a forge or furnace bellowsj which hare de- 
ceived many by their slow regular motion. 



CHAP. III.] HYDRAULICS. 155 

l 

PART III. 

ARTICLE 69. 



OF THE CONSTRUCTION AND EFFECTS OF WIND-MILL SAILS. 

" In trying experiments on wind-mill sails, the wind 
itself is too uncertain to answer the purpose ; we must, 
therefore, have recourse to artificial wind. 

This may be done two ways ; either by causing the air 
to move against the machine, or the machine to move 
against the air. To cause the air to move against the 
machine in a sufficient column, with steadiness and the 
requisite velocity, is not easily put in practice : To carry 
the machine forward in a right line against the air, would 
require a larger room than I could conveniently meet 
with. What I found most practicable, therefore, was to 
carry the axis whereon the sails were to be fixed progres- 
sively round in the circumference of a large circle. Upon 
this idea the machine was constructed.! 

Specimen of a Set of Experiments. 

Radius of the sails, - - - - 21 inches. 
Length of do. in cloth, - - - - 18 
Breadth of do. ----- 5,6 

i Angle at the extremity, - - - 10 degs. 
J < Do. at the greatest inclination, - 25 

( 20 turns of the sails raised the weight, 11,3 inch. 
Velocity of the centre of the sails in the cir- ) 

cumference of the great circle in a second, > 6 feet. 

in which the machine was carried round, j 
Continuance of the experiment, - - 52 seconds. 

* Read May 31st and June 14th, 1759, in the Philosophical Society of London. 

1 1 decline giving any description or draught of this machine, as I have not 
room; hut I may say, that it was constructed so as to wind'tip a weight, (as did 
the other model,) in order to find the effect of the power. I also insert a speci- 
men of a set of experiments, which I fear will not be well understood for want of 
a full explanation of the machine. 

t In the following experiments, the angle of the sails is accounted from the plane 
of their motion; that is, when they stand at right angles to the axis, their angle 
is denoted deg.; this notation being agreeable to the language of practitioners, who 
call the angle so denoted the weather of the sail; which they denominate greater 
or less, according to the quantity of the angle. 



56 




HYDRAULICS. 


[chap. I 


No. 


Weight in the scale, 


Turns, 


Product. 


1 


lbs. 


108 





3 


6 


85 


510 


3 


u 2 


81 


526| 


4 


7 


73 


546 


5 


71 


73 


547 1 maxim. 


6 


8 2 


65 


520 


7 


9 









The product was found by simply multiplying the weight 
in the scale by the number of turns. 

By this set of experiments it appears, that the maxi- 
mum velocity is 2-3ds of the greatest velocity, and that 
the ratio of the greatest load to that of the maximum is 
as 9 to 7,5, but, by adding the weight of the scale and 
friction to the load, the ratio turns out to be as 10:8,4, 
or 5 to 4, nearly. The following table is the result of 19 
similar sets of experiments. 

By the following table it appears that the most general 
ratio between the velocity of the sails unloaded and when 
loaded to a maximum, is 3 to 2, nearly. 

And the ratio between the greatest load and the load at 
a maximum (taking such experiments where the sails 
ariswered best,) is at a medium, about as 6 to 5, nearly. 

And that the kind of sails used in the 15th and 16th 
experiments are best of all, because they produce the 
greatest effect or product, in proportion to their quantity 
of surface, as appears in column 12. 



CHAP. III.] 



HYDRAULICS. 



157 



TABLE IV. 

Containing Nineteen sets of Experiments on Wind-mill sails of various Structures, 
Positions, and Quantities of Surface. 



H 3 


> 


O 


H 


H 


f 


Q 


N3 


O 


Sd 


m 




w 


CD 


3 

CD 


B 

era 

CD 

p 


1-! 
CD 
P 

CD 

tn 


S3 

3 

w 

O 
"5 


s 

CO , 

p 


o 
p 

a-, 
p 

p 


CD 
P 

CD 
CO 
e-t- 


o 

o 


p 


p 

it 


5' 
o 




o' 
o 

M5 


o 




CD 


3 
00 


CD 


P 

3 


3 
p 


O 
P 




o 

en 


S-' CD 
^ CM 


P S3" 
(-. CD 

P era 




CD 














x 






S3 










p_ 

CO 

3 
p 

&. 

CD 




* 

CD 

3. 

CD* 




P. 
93 

o 
p 
p- 

CD 


1 

i 


3 



3 






H 

o 

CD 


P 
CD 

3 S- 

*.£ 

3 cT 

S3 O 


3 g ■ 
p rt 

X CD 
>-■ en 

3 *~ 
1 g 


&. en 

E c! 
O ~s 

o 

CD 
ST 


CD 
O 








Q- 












3 4 


& 




cr 


J-tj 




















o 

B" 
CD 


CD 

cT 

P 




6 






Deg. 


Deg. 






lbs. 


lbs. 




sq.in 








I. 


1 


35° 


35° 


66 


42 


7.56 


12.59 


318 


404 


10:7 


10:6 


10: 


7. 9 




2 


12 


12 




70 


6.3 


7.56 


441 


404 




10:8.3 


1U 


10. 1 


II. 


3 


15 


15 


105 69 


6.72 


8.12 


464 


404 


10:6.6 


10:8.3 


10: 


10.15 




4 
5 


18 


18 


96 


66 


7.0 


9.81 


462 


404 


10:7 


10:7.1 


10 


10.15 


9 


26.5 




66 


7.0 




462 


404 






10 


11. 4 


III. 


6 


12 


29.5 




70.5 


7.35 




518 


404 






10 


12. S 




1 


15 


32.5 




63.5 


8.3 




527 


404 






10 


:13. 




8 





15 


120 


93 


4.75 


5.31 


442 


404 


10:7.7 


10:8.9 


10 


11. 




9 


3 


18 


120J79 


7.0 


8.12 


553 


404 


10:6.6 


10:8.6 


10 


13. 7 


IV. 


10 


5 


20 


78 


7.5 


8.12 


585 


404 




10:9.2 


10 


14. 5 


11 


7.5 


22.5 


113 77 


8.3 


9.81 


639 


404 


10:6.8 


10:8.5 


10 


15. 8 




IS 


10 


25 


10873 


8.69 


10.37 


634 


401 


10:6.8 


10:8.4 


10 


15. 7 




13 


12 


27 


100 66 


8.41 


10.94 


580 
799 


404 
505 


10:6.6 
10:6.1 


10:7.7 
10:8.5 


10 


14. 4 




11 


7.5 


22.5 


123 75 


10.65 


12.59 


1!) 


15. 8 


V. 


15 


10 


25 


11774 


11.08 


13.69 


820 


505 


10:6.3 


10 


8.1 


10 


16. 2 


16 


12 


27 


114 66 


12.09 


14.23 


799 


505 


10:5.8 


10 


8.4 


10 


15. 8 




17 


15 


30 


96 63 


12.09 


14.78 


762 


505 


10:6.6 


10 


8.2 


10 


.15. 1 


VI. 


1812 


22 


10564.5 


1 6. 42 


27.87 


1059 


854 


10:6.1 


10:5.9 


10 


12. 4 


19 


12 


22 


99 64.5 


18.06 




1165 


1146 


10:5.9 




10 


10. 1 




1 


2 


3 


4 5 


6 


7 


8 


9 


10 


11 


12 



I. Plain sails at an angle of 55 degrees. 

II. Plain sails weathered according to common practice. 

III. Weathered according to Maclaurin's theorem. 

IV Weathered in the Dutch manner, tried in various positions. 

V. Weathered in the Dutch manner, but enlarged towards the extremities. 

VI. Eight sails, being sectors or ellipses in their best positions. 



15S 



HYDRAULICS. 



[chap. III. 



TABLE V. 



Containing the result of six sets of experiments, made for determining the diffe- 
rence of effect according to the different velocity of the wind. 



Ratio of the greatest load to the load at a 
maximum. 




CO -* 
00 en 

o o 




U0 t-- 

00 CO 

o o 


-* 


Ratio of the greatest velocity to the ve- 
locity at a maximum. 




C73 OS 

co ui 

o o 




t- 0J 

co co 

o © 


CO 


Ratio of the two products. 




CO 

eg 

o 


CO 

© 


CO 

CM 

2 


CM 


Product of the lesser load and greater 
velocity. 





US 

o 

00 

o~ 

00 
I— 1 


CM 
CO 
CO 

o~ 

CO 

I— 1 


LO 

© 

CO - 


© 


Turns of the sails therewith. 


Maximum load for half the velocity. 






CM 

CO 


CO 

o 


© 


Product. 




O CO 

05 O 

CM o 
CM 


© 00 
O t- 
CO CM 


O ^CH 

CO o 
CM 


00 


Greatest load. 




t- co 

CO o 

16 o6 




00 CO 

ITS -H 

CM 


b- 


Load at the maximum. 


CO 
X2 


t~ CM 

•^ to 


CM CM 

CO U0 


CO rH 
O CO 

>o 00 


co 


Turns of the sails at a maximum. 




CO CM 
■XI CM 


U0 o 

CO CO 


i— i o 
CO CO 


Turns of the sails unloaded. 




co t- 

Ci o 

CM 




— 'Xl 

en t- 

T— I 


■* 


Velocity of the wheel in a second. 




-KM 
"* OS 

tp CO 


"PI 

•*# © 

t}< co 


"KM 

■* OO 
■«* 00 


CO 


. Angle at the extremity. 




to ia 


lO UO 


© o 


CM 


Number. 




— I CM 


C0-* 


m to 


- 



N. B. — The sails were of the same size and kind as those of Nos. 10, 1 1, and 12, 
Table IV. Continuance of the experiment one minute. 



CHAP. III.] HYDRAULICS. 159 

Concerning the Effects of Sails according to the different 
Velocity of' the Wind. 

" From the foregoing table the following maxims are 
deduced. 

Maxim I. The velocity of wind-mill sails, whether un- 
loaded or loaded, so as to produce a maximum, is nearly 
as the velocity of the wind, their shape and position beino- 
the same. 

This appears by comparing the respective numbers of 
columns 4 and 5, table V., wherein those numbers 2, 4, 
and 6, ought to be double of No. 1, 3, and 5, and are as 
nearly so as can be expected by the experiments. 

Maxim II. The load at the maximum is nearly, but 
somewhat less than, as the square of the velocity of the 
wind, the shape and position of the sails being the same. 

This appears by comparing No. 2, 4, and 6, in column 
6, with 1,3, and 5, wherein the former ought to be quad- 
ruple of the latter, (as the velocity is double,) and are as 
nearly so as can be expected. 

Maxim III. The effects of the same sails at a maximum 
are nearly, but somewhat less than, as the cubes of the 
velocity of the wind.* 

It has been shown, maxim I. that the velocity of sails 
at a maximum is nearly as the velocity of the wind; and 
by maxim II. that the load at the maximum, is nearly as 
the square of the same velocity. If those two maxims 
would hold precisely, it would be a consequence that the 
effect would be in a triplicate ratio thereof. How this 
agrees with experiment will appear by comparing the 
products in column 8, wherein those of No. 2, 4, and 6, 
(the velocity of the wind being double,) ought to be octu- 
ple of those of No. 1, 3, and 5, and are nearly so. 

Maxim IV. The load of the same sails at the maximum 
is nearly as the squares of, and their effects as the cubes 
of, their number of turns in a given time. 

* This confirms the 7th law of spouting fluids. 



160 HYDRAULICS. [CHAP. III. 

This maxim may be esteemed a consequence of the 
three preceding ones." 

These 4 maxims agree with and confirm the 4 maxims 
concerning the effects of spouting fluids acting on under- 
shot mills; and, I think, sufficiently confirm as a law of 
motion, that the effect produced, if not the instant mo- 
mentum of a body in motion, is as- the square of its velo- 
city, as asserted by the Dutch and Italian philosophers. 
Smeaton says that by several trials in large, he has found 
the following angles to answer as well as any: — 

" The radius is supposed to be divided into 6 parts, and 
1 -6th, reckoning from the centre is called 1, the extremity 
being denoted 6. 



No. 


An 


gle with the 


axis. 


Angle w 


1th the plane of motion. 


1 




72° 






18° 


2 




71 






19 


o 
u 




72 






IS middle. 


4 




74 






16 


5 




771 






1Q1 

l^ 2 


6 




83 






7 extremity." 



He seems to prefer the sails being largest at ths ex- 
tremities. 



END OF PART FIRST. 



THE 



YOUNG MILL-WRIGHT'S GUIDE 



PART THE SECOND. 



INTRODUCTION. 

What has been said in the first part was meant to 
establish theories, and to furnish easy rules. In this part 
I mean to show their practical application, in as concise 
a manner as possible, referring only to the articles in the 
first part, where the reasons and demonstrations are 
given. 

This part is particularly intended for the help of young 
and practical mill-wrights, whose time will not admit of 
a full investigation of those principles and theories, which 
have been laid down; I shall, therefore, endeavour to 
reduce the substance of all that has been said to a few 
table rules, and short directions, which, if found to agree 
with experience, will be sufficient for the practitioner. 



CHAPTER IV. 

OF THE DIFFERENT KINDS OF MILLS. 

ARTICLE 70. 
OF UNDERSHOT MILLS. 

Undershot wheels move by the percussion or stroke of. 
the water, and are only half as powerful as other wheels 
11 



162 OF UNDERSHOT MILLS. [CHAP. IV. 

that are moved by the gravity of the water. See Art. 9. 
Therefore, this construction ought not to be adopted ex- 
cept where there is but little fall, or great plenty of 
water. The undershot wheel, and all others that move 
by percussion, should move with a velocity nearly equal 
to two-thirds of the velocity of the water. See Art. 42, 
Fig. 28, Plate IV., represents this construction. 

For a rule for finding the velocity of the water, under 
any given head, see Art. 51. Upon the principles, and 
by the rule, given in that article, is formed the following 
table of the velocity of spouting water, under different 
heads, from one to twenty-five feet high above the centre 
of the issue; to which is added the velocity of the wheel 
suitable thereto, and the number of revolutions a wheel of 
fifteen feet diameter (which 1 esteem a good size) will 
revolve in a minute; also the number of cogs and rounds 
in the wheels both for double and single gears, so as 
to produce about ninety-seven or one hundred revolu- 
tions per minute, for a five feet stone, which I think a 
good motion and size for a mill stone, grinding for mer- 
chantable flour. 

That the reader may fully understand how the follow- 
ing table is calculated, let him observe, 

1. That, by Art. 42, the velocity of the wheel must be 
just 577 thousandth parts of the velocity of the water; 
therefore, if the velocity of the water, per second, be mul- 
tiplied by ,577, the product will be the maximum velocity 
of the wheel, or velocity that will produce the greatest 
effect, which is the third column in the table. 

2. The velocity of the wheel per second, multiplied by 
60, produces the distance the circumference moves per 
minute which divided by 47,1 feet, the circumference of 
a 15 feet wheel, gives the number of revolutions of the 
wheel per minute, which is the fourth column. 

3. That, by Art. 20 and 74, the number of revolutions 
of the wheel per minute, multiplied by the number of 
cogs in all the driving wheels, successively, and that 
product divided by the product of the number of cogs 
in all the leading wheels, multiplied successively, the 
quotient is the number of revolutions of the stones per 



CHAP. IV.] OF UNDERSHOT MILLS. 163 

minute which is found in the ninth and twelfth co- 
lumns. 

4. The cubochs of power required to drive the stone 
being by Art. 61, equal to 111,78 cubochs per second, 
which divded by half the head of water, added to all 
the fall, (if any,) being the virtual or effective head by 
Art. 61, gives the quantity of water, in cubic feet re- 
quired per second, which is found in the thirteenth co- 
lumn. 

5. The quantity required, divided by the velocity with 
which it is to issue, gives the area of the apertures of the 
gate, and is shown in the fourteenth column. 

6. The quantity required, divided by the velocity 
proper for the water to move along the canal, gives the 
area of the section of the canal; as in the fifteenth co- 
lumn. 

7. Having obtained their areas, it is easy, by Art. 65, 
to determine the width and depth, which may be varied 
to suit other circumstances. 



164 



OF UNDERSHOT MILLS. 



[chap. IV. 



THE MILL-WRIGHT'S TABLE 

FOR 

UNDERSHOT MILLS, 

CALCULATED FOR A WATER WHEEL OF FIFTEEN FEET, AND 
STONES OF FIVE FEET DIAMETER. 



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112 


22 


54 


16 


191.6 


_ 






cub. ft. 


sup ■ ft. 


sup ft 


feet. 
V 


feet. 
8.1 


feet. 
4.67 


5.94 




223.5 


27.5 


149. 


2 


11.4 


6.57 


8.36 


96 


•23 


54 


19 


99 








111.78 


9-8 


74.5 


3 


14. 


8.07 


10.28 


88 


25 


54 


19 


100.5 








74.52 


4.6 


43. 


4 


16.2 


9.34 


11.19 


78 


23 


48 


20 


97 








55.89 


3.45 


37.26 


5 


18. 


10.38 


13.22 


66 


24 


48 


18 


97 


112 


15 


98.66 


44.7 


2.48 


29.8 


6 


19.84 


11.44 


14.6 


66 


24 


48 


20 


90,2 


112 


17 


96.2 


37.26 


1.9 


24.84 


ft- 


21.43 


12.36 


15.74 


66 


25 


44 


19 


96.2 


104 


17 


96.2 


31.9 


, "1.48 


21.26 


8 


22.8 


13.15 


16.75 


66 


25 


44 


20 


97.2 


96 


k; 


100. 


27.94 


1.22 


18.6 


9 


24.3 


14.02 


17.86 


66 


26 


42 


19 


100.2 


96 


17 


100.8 


24.84 


].02 


16.56 


10 


25.54 


14.73; 18.78 


60 


25 


44 


20 


99 


96 


18 


100. 


22.89 


.9 


15.26 


11 


26.73 


15.42 


19.7 


60 


26 


44 


20 


100 


96 


19 


99.5 


20.32 


.76 


13.54 


12 


28. 


16.16 


20.5 


60 


•27 


44 


20 


100 


96 


20 


98.4 


18.63 


.66 


12.42 


13 


29.16 


16.82 


21.42 


60 


27 


42 


•20 


99.8 


96 


21 


102.6 


16.27 


.56 


10.8 


14 


30.2 


17.42 


22.19 


60 


28 


42 


2D 


99 


88 


•20 


97.63 


15.94 


.53 


10.6 


15 


31.34 


18.08 


23,03 


60 


29 


42 


21) 


99 


88 


21 


96.5 


14.9 


.47 


9.93 


16 


32.4 


18.69 


23.8 












88 


21 


99,7 


13.97 


.43 


9.31 


17 


33.32 


19.22 


24.48 












84 


21 


97.9 


13.14 


.39 


8.76 


18 


34.34 


19.81 


25.23 












80 


21 


96.1 


12.42 


.36 


8.28 


19 


35. is 


20.29 


25.82 












so 


21 


98.3 


11.76 


.33 


7.84 


20 


36.2 


20.88 


26.6 












78 


21 


98.3 


11.17 


.3 


7.4 


21 


37.11 


21.41 


27.26 












7d 


22 


97. 


10.64 


.29 


7.1 


22 


37.9H 


21.86 


27.84 












78 


22 


98.6 


10.16 


.26 


6.77 


23 


38.79 


22.3fe 


28.5 












7-2 


■21 


97.7 


9.72 


.25 


6.48 


24 


39.6S 


22.90 


29.17 












66 


20 


96.2 


9.32 


.23 


6.21 


25 
1 


40.5 

2 


23.36 
3 


29.70 
4 


U 


6 


7 


8 


9 


6018 


99. 


8.94 


.22 


5.96 
15 


1 10 


In 


12 


13 


14 



CHAP. IV.] OF UNDERSHOT MILLS. 165 

It must be observed, that five feet fall is the least that a 
single gear can be built on, to keep the cog-wheel clear 
of the water, and give the stone sufficient motion. 

Although double gear is calculated to fifteen feet fall, 
yet I do not recommend them above ten feet, unless for 
some particular convenience, such as for two pairs of 
stones to one wheel, &c, &c. The number of cogs in 
the wheels is even, and is thus suited to eight, six, or four 
arms, so as not to pass through any of them, this being 
the common practice; but when the motion cannot be 
obtained without a trundle that will cause the same cogs 
and rounds to meet too often, such as 16 into 96, which 
will meet every revolution of the cog-wheel, or 18 to 96, 
which will meet every third revolution, I advise the put- 
ting in either of one more or one less, as may best suit 
the motion, which will cause them to change oftener. 
See Art. 82. 

It should be recollected that the friction at the aperture 
of the gate will greatly diminish both the velocity and 
power of the water, where the head is great, if the gate 
be made of the usual form, that is, wide and shallow. 
Where the head is great, the friction will be great. See 
Art. 55 : therefore, the wheel must be narrow, and the 
aperture of the gate of a square form, in order to avoid 
the friction and loss in a wide wheel, especially if it dp 
not run very closely to the sheeting. 

Use of the Table, 

Having levelled your mill-seat carefully, and finding 
such fall and quantity of water as determines you to 
make choice of an undershot wheel; for instance, suppose 
6 feet fall, and about 45 cubic feet of water per second, 
which you may find in the way directed in Art. 53; cast 
off about one foot for fall in the tail-race below the bot- 
tom of the wheel, if subject to back-water, which leaves 
you 5 feet head; then look for 5 feet head in the first 
column of the table, and against it are all the calculations 
for a 15 feet water-wheel, and 5 feet stones; in the thir- 
teenth column you have 44,7 cubic feet of water, which 
shows you have enough for a pair of five feet stones ; and 



166 OE UNDERSHOT MILLS. [CHAP. IV. 

the velocity of the water will be 18 feet per second, the 
velocity of the wheel 10,38 feet per second, and it will 
revolve 13,22 times per minute. If you choose double 
gear, then 66 cogs in the master cog-wheel, 24 rounds 
in the wallower, 48 cogs in the counter cog-wheel, and 
IS rounds in the trundle will give the stone 97 revolu- 
tions in a minute; if single gear, 112 cogs and 15 rounds 
give 98,66 revolutions in a minute; it will require 44,7 
cubic feet of water per second; the size of the gate must 
be 2,48 feet; which will be about 4 feet wide, and ,62 
feet, or about 7| inches deep : the size of the canal must 
be 29,8 feet; that is, about 3 feet deep, and 9,93 or nearly 
10 feet wide. If you choose single gear, you must make 
your water-wheel much smajler, say 7|, the half of 15 
feet, then the cog-wheel must have half the number of 
cogs, the trundle head the same, the spindle will be longer, 
and the husk lower; the mill will then be full as good as 
with double gear: in tlje case supposed, however, a cog- 
wheel of 66 cogs would not answer, because it would 
reach the water; but where the head is ten or twelve 
feet, it will do very well. 

If you choose stones, or water-wheels, of other sizes, 
it will be easy, by similar rules, to proportion the whole 
to suit, seeing you have the velocity of the periphery of 
a wheel to any size.* 



* One advantage large wheels have over small ones is, that they cast off the 
hack- water much better. The buckets of the low wheel will lift the water much 
more than those of the high wheel; because the nearer the water rises to the cen- 
tre of the wheel, the nearer the buckets approach the horizontal or lifting position. 

To make a wheel cast off back-water, some mill-wrights fix the sheeting be- 
low the wheel, with joints and hinges, so that the end down stream can be raised 
so as to shoot the water, as it leaves the wheel, on to the surface of the back- 
water, and thus roll it from the wheel : it is thought that it will drive off the back- 
water much better. 

Plate IV. fig. 28, shows an undershot wheel. Some mill-wrights prefer to slant 
the forebay under the wheel, as in the figure, that the gate may be drawn near the 
floats ; because they think that the water acts with more power near the gate, than 
at a distance; which appears to be the case when we consider, that the nearer we 
approach the gate, the nearer the column of water approaches to what is called a 
perfectly definite quantity. See Art. 59. 

Others, again, say, that it acquires equal power of descending the shute. (It 
will certainly acquire equal velocity, abating only for the friction of the shute and 
the air.) When the shute has a considerable descent, the greater the distance 
from the gate, the greater the velocity and power of the water; but where the 
descent of the shute is not sufficient to overcome the friction of the air, &c, then 



CHAP. IV.] OF TUB MILLS. 167 

Observations on the Table. 

1. The table is calculated for an undershot wheel con- 
structed, and the water shot on, as in Plate IV. fig. 28. 
The head is counted from the point of impact I., and the 
motion of the wheel at a maximum, about ,58 of the velo- 
city of the water; but when there is plenty of water and 
great head, the wheel will run best at about ,66 or two- 
thirds of the velocity of the water; therefore, the stones 
will incline to run faster than in the table, in the ratio of 
58 to 66, nearly ; for which reason, I have set the motion 
of 5 feet stones under 100 revolutions in a minute, which 
is slower than common practice; they will incline to run 
between 96 and 110 revolutions. 

2. I have taken half of the whole head above the point 
of impact, for the virtual or effective head by Art. 53, 
which I apprehend will be too little in very low heads, 
and, perhaps, too much in high ones. As the principle 
of non-elasticity does not seem to operate against the 
power so much in low as in high heads; therefore, if the 
head be only 1 foot, it may not require 223,5 cubic feet 
of water per second, and if 20 feet may require more than 
11,17 cubic feet of water per second, the quantities given 
in the table. 



article 71. 



OF TUB MILLS. 



A tub mill has a horizontal water-wheel, that is acted 
on by the percussion of the water altogether; the shaft is 

the nearer the gate, the greater the velocity and power of the water ; which argues 
in favour of drawing the gate near the floats. Yet, where the fall is great, or water 
plenty, and the expense of a deep penstock considerahle, the small difference of 
power is not worth the expense of thus obtaining it. In these cases, it is best to 
have a shallow penstock, and a long shute to convey the water down to the wheel, 
drawing the gate at the top of the shute : this is frequently done to save expense in 
building saw-mills, with flutter-wheels, which are small undershot wheels, fixed 
on a crank shaft, and made so small as to obtain a sufficient number of strokes of 
the saw in a minute, say about 120. This wheel is to be of such a size as is cal- 
culated to suit the velocity of the water at the point of impact, so as to make that 
number of revolutions (120) in a minute. 

* Thomas Ellicott's method of shooting the water on an undershot-wheel, where 
the fall is great, is shown in Plate 13, fig. 6. 



168 OF TUB MILLS. [CHAP. IT. 

vertical, carrying the stone on the top of it, and serves 
in place of a spindle ; the lower end of this shaft is set in 
a step fixed in a bridge-tree, by which the stone is raised 
and lowered, as by the bridge-tree of other mills; the wa- 
ter is shot on the upper side of the wheel, in the direc- 
tion of a tangent with its circumference. See fig. 29, 
Plate IV., which is a top view of the tub-wheel, and fig. 
39, which is a side view of it, with the stone on the top 
of the shaft, bridge-tree, &c. The wheel runs in a hoop, 
like a mill-stone hoop, projecting so far above the wheel 
as to prevent the water from shooting over the wheel, 
and whirls it about until it strikes the buckets, because 
the water is shot on in a deep narrow column, 9 inches 
wide and 18 inches deep, to drive a 5 feet stone, with 
8 feet head — the whole of this column cannot enter the 
buckets until a part has passed half way round the 
wheel, so that there are always nearly half the buckets 
struck at once ; the buckets are set obliquely, that the 
water may strike them at right angles. See Plate IV., 
fig. 30. As soon, as it strikes, it escapes under the wheel, 
in every direction, as in fig. 29. # 



* Note. That in Plate IV. fig. 30, 1 have allowed the gate to be drawn inside 
of the penstock, and not in the shute near the wheel, as is the common practice ; 
because the water will leak out much alongside of the gate, if drawn in the shute. 
But here we must consider that the gate must always be full drawn, and the quan- 
tity of water regulated by a regulator in the shute near the wheel; so that the 
shute will be perfectly full, and pressed with the whole weight of the head, else 
a great part of the power may be lost. 

To show this more plainly, suppose the long shute A, from the high head (shown 
by dotted lines) of the undershot mill, fig. 28, be made tight by being covered at 
top, then, if we draw the gate A, but not fully, and if the shute at bottom be large 
enough to vent all the water that issues through the gate when the shute is full 
to A, then it cannot fill higher than A: therefore, all that part of the head above 
A is lost, it being of no other service than to supply the shute, and keep it full 
to A, and the head from A to the wheel, is all that acts on the wheel. 

Again, when we shut the gate, the shute cannot run empty, because it would 
leave a vacuum in the head of the shute at A ; therefore, the pressure of the atmo- 
sphere resists the running out of the water from the shute, and whatever head of 
water is in the shute when the gate is shut, will balance its weight of the pres- 
sure of the atmosphere, and prevent it from acting on the lower side of the gate, 
which will cause it to be very hard to draw. For, suppose 11 feet head of water 
to be in the shute when the gate was shut, its pressure is equal to about 5 lbs. per 
square inch; then, if the gate be 48 by 6 inches, which is equal to 288 inches, this 
multiplied by 5, is equal to 1440 lbs. the additional pressure on the gate. 

Again, if the gate be full drawn, and the shute be not much larger at the up- 
per than the lower end, these defects will cause much loss of power. To remedy 
all this, put the gate H at the bottom of the shute, to regulate the quantity of water 
by, and make a valve at A to shut on the inside of the shute, like the valve of a 
pair of bellows, which will close when the gate A is drawn, and open when the 



CHAP. IV.] OF TUB MILLS. 169 

The disadvantages of these wheels are, 

1. Under the best construction, the water does not act 
to advantage on them; and it is in general necessary to 
make them so small, in order to give velocity to the stone, 
that the buckets take up a third part of their diameter. 

2. The water acts with less power than on undershot 
wheels, as it is less confined at the time of striking the 
wheel, and its non-elastic principle operates more fully. 

3. If the head be low, it is with difficulty we can put 
a sufficient quantity of water to act on them so as to drive 
them with sufficient power; I, therefore, advise to let the 
water strike on them in two places ; as in Plate IV. fig. 
29; the apertures need then only be about 6 by 13 inches 
each, instead of 9 by 18; they will then operate to more 
advantage, as nearly all the buckets will be acted on at 
once. 

Their advantages are, 

Their exceeding simplicity and cheapness, having no 
cogs nor rounds to be kept in repair, their wearing parts 
are few, and have but little friction; the step-gudgeon 
runs under water, therefore, if well-fixed, it will not get 
out of order in a long time; they will move with suffi- 
cient velocity and power with 9 or 10 feet total fall, if 
there be plenty of water; and, if they be well fixed, they 
will not require much more water than undershot wheels; 
they are, therefore, preferable in all seats which have a 
surplus of water, and above 8 feet fall. 

In order that the reader may fully understand how 
the following table for tub-mills is calculated, let him 
consider, 

1. That the tub-wheel moves altogether by percussion, 
the water flying clear of the wheel the instant it strikes, 
and that it is better, (by Art. 70,) for such wheels to move 
faster than the calculated maximum velocity: therefore, 
instead of ,577, we will allow them to move ,66 velocity 
of the water; then multiplying the velocity of the water 

gate shuts, and let air into the shute; this plan will do better for saw-mills with 
flutter-wheels, or tub-mills, than long open shutes, as by it we avoid the friction 
of the shute and the resistance of the air. 

To understand what is here said, the reader must be acquainted with the theory 
of the pressure of the atmosphere, vacuums, &c. See these subjects touched on 
in Art. 56. 



170 OF TUB MILLS [CHAP. IV. 

by ,66, gives the velocity of the wheel, at the centre of 
the buckets, which constitute the third column in the 
table. 

2. The velocity of the wheel per second, multiplied by 
60, and divided by the number of revolutions the stone 
is to make in a minute, gives the circumference of the 
wheel at the centre of the buckets; which circumference, 
multiplied by 7, and divided by 22, gives the diameter 
from the centre of the buckets, to produce the number of 
revolutions required: which are contained in the 4th, 6th, 
and 7th columns. 

3. The cubochs of power required, by Art. 63, to drive 
the stone, divided by half the head, give the cubic feet of 
water required to produce said power; which are found 
in the 8th and 10th columns. 

4. The cubic feet of water, divided by the velocity, 
will give the sum of the apertures of the gates ; which 
are shown in the 9th and 11th columns. 

5. The cubic feet of water, divided b}^ 1,5 feet, the velo- 
city of the water in the canal, gives the area of a sec- 
tion of the canal; which is shown in the 12th and 13th 
columns. 

v 6. For the quantity of water, aperture of gate, and 
size of canal, for 5 feet stones, see table for undershot 
millss in Art. 70, 



CHAP. IV.] 



OF TUB MILLS. 



171 



THE MILL-WRIGHT'S TABLE 



TUB MILLS 



< 



feet. 



2. a. 



3 Z 

SB CD 



CD 



S - 3 

Is 

to j- 
to r* 

CD o 



•22. 
24; 

2.3. 
2G. 



1228. 



13 
14 
15 
Ifi 
1? 
18 
19 
20 



feet. 



feet. 



2.17 
2.5 
2.63 
2.75 



1823 
2 23 



.9 

.01 

• 12 

.24 

3.34 

3.43 

3.54 



21 3. 63 
89 3. 71 



feet. 



feet. 



feet. 



2. 73|3 
3.12 3 
3.28 
3.44 
3.6 
3.74 
3.9 
4.03 
4. 12 
4.25 
4.41 
4.52 
.62 



3 3.9 

68'4. 37 



01 



4.59 
4.8 



1 

5 

5 

5 

5 

18 5.95 
326. 18 
47 6.33 
49 6.47 



O 



cub. ft, 



17.34 

15.41 

13.87 

12.61 

11.56 

10.67 

9.9 

9.21 

8.67 

8. 16 

7.7 

7.3 

6.93 



a 



su. ft. cub. ft. 



,7640.9 



36.35 
32.72 
29. 74 
27.26 
25. 17 
23.36 
21. 93 



27|20. 45 



19.24 

18. 18 

17. 

16.36 

10 





TO 






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su. ft. sup. ft 



7911. 

5 10. 
28 9 
11 

97 

st; 

77 

7 

6 

57 
52 

48 
45 



sup. ft 



11 



5627. 3 
3 J24. 23 

25,21.7 



12 



19.83 

18. 17 

16.8 

15.56 

14.62 

13.6 

12.15 

12.12 

11.33 

10.9 

13 



172 OF BREAST MILLS. [CHAP. IV. 

Use of the Table for Tub Mills. 

Having levelled your mill-seat, and found that you 
have above 8 feet fall, and plenty of water, and wishing 
to build a mill on the simplest, cheapest, and best con- 
struction to suit your seat, you will, of course, make choice 
of a tub mill. 

Cast off 1 foot for fall in the tail-race, below the bottom 
of the wheel, if it be subject to back water, and 9 inches 
for the wheel; then suppose you have 9 feet left for head 
above the wheel; look in the table against 9 feet head, 
and you have all the calculations necessary for 4, 5, 6, and 
7 feet stones, the quantity of water required to drive them, 
the sum of the areas of the* apertures, and the areas of 
the canals. 

If you choose stones of any other size, you can easily 
proportion the parts to suit, by the rules by which the 
table is calculated. 

Let it be recollected, however, that it is a very common 
error, to build tub mills in situations where they must 
fail during a dry season. They are suited to those places 
only where water runs to waste during the whole year. 
There are hundreds of such mills in the United States 
which are useless at the season when they are most 
needed, whilst a well-constructed overshot, breast, or 
pitch-back wheel, might be kept constantly running. 



article 72. 

OF BREAST MILLS. 

Breast wheels, which have the water shut on them in 
a tangential direction, are acted on by the principles both 
of percussion and of gravity ; all that part above the point 
of impact, called head, acts by percussion; and all that 
part below said point, called fall, acts by gravity. 

We are obliged, in this structure of breast mills, to 
use more head than will act to advantage ; because we 
cannot strike the water on the wheel, in a true tangen- 



CHAP. IV.] OF BREAST MILLS. 173 

tial direction, higher than I. the point of impact, as 
shown in Plate IV., fig. 31, which is a breast wheel with 
12 feet perpendicular descent, 6,5 feet of which are above 
the point I., as head, and 5,5 feet below, as fall. The 
upper end of the shute that carries the water down to the 
wheel, must project some inches above the point of the 
gate when full drawn, otherwise the water will strike 
towards the centre of the wheel ; and it must not project 
too high, or else the water in the penstock will not come 
fast enough into the shute when the head sinks a little. 
The bottom of the penstock is a little below the top end 
of the shute, to leave room for stones and gravel to settle, 
and prevent them from getting into the gate. 

We might lay the water on higher, by setting the top 
of the penstock close to the wheel, and using a sliding 
gate at bottom, as shown by the dotted lines; but this is 
not approved of in practice. See Ellicott's mode, Plate 
XV., fig. 1. 

But if the water in the penstock be nearly as high as 
the wheel, it may be carried over; as shown by the up- 
per dotted lines, and shot on backwards, making that part 
next the wheel, the shute to guide the water into the 
wheel, and the gate very narrow or shallow, allowing the 
water to run over the top of it when drawn: by this 
method (called pitch-back) the head may be reduced to 
the same as it is for an overshot wheel; and then the 
motion of the circumference of the wheel will be equal to 
the motion of an overshot wheel, whose diameter is equal 
to the fall below the point of impact, and their powers 
will be equal. 

This structure of a wheel, Plate IV., fig. 31, I view as 
a good one for the following reasons, namely: — 

1. The buckets, or floats, receive the percussion of the 
water at right angles, which is the best direction possi- 
ble. 

2. It prevents the water from flying towards the cen- 
tre of the wheel without reacting against the bottom of 
the buckets, and retains it in the wheel, to act by its 
gravity in its descent, after the stroke. 

3. It admits air, and discharges the water freefy, with- 



174 OF BREAST MILLS. [CHAP. IV. 

out lifting it at bottom; and this is an important advan- 
tage, because, if the buckets of a wheel be tight, and the 
wheel made a little in back-water, they will lift the wa- 
ter to a considerable distance as they empty; the pres- 
sure of the atmosphere then prevents the water from 
leaving the buckets freely, and it requires a great force 
to lift them out of the water with the velocity of the 
wheel.; this may be proved by dipping a common water- 
bucket into the water, and lifting it out, bottom up, with 
a quick motion; you have to lift not only the water in the 
bucket, but it appears to suck much more up after it; 
which is the effect of the pressure of the atmosphere. 
See Art. 56. This shows the necessity of air-holes to 
let air into the buckets, that the water may have liberty 
to escape freely. 

Its disadvantages are, 

1. It loses much water, if it be not kept closely to the 
sheeting. And, 

2. It requires too great a part of the total fall to be used 
as head, which is a loss of power, one footfall being equal 
in power to two feet head. 

Plate IV. fig. 32, is a draught, showing the position of 
the shute for striking the water on a wheel in a tangent, 
for all the total perpendicular descents from 6 to 15 feet; 
the points of impact are numbered inside the fig. with 
the number of the total fall, for each respectively. The 
top of the shute is only about 15 inches from the wheel, 
in order to set the point of impact as high as possible, 
allowing 3 feet above the upper end of the shute to the 
top of the water in the penstock, which is little enough, 
when the head is to be often run down any considerable 
distance; but where the stream is steady, being always 
nearly the same height in the penstock, 2 feet would be 
sufficient, especially in the greatest total falls. Where 
the quantity is less, raising the shute 1 foot would also 
raise the point of impact nearly the same, and increase 
the power, because 1 foot fall is equal in power to 2 feet 
head, by Art. 61. 

On these principles, to suit the applications of water, 
as represented by fig. 32, I have calculated the follow- 



CHAP. IV.] OF BREAST MILLS. I?5 

ing table for breast mills. And, in order that the reader 
may fully understand the principles on which it is calcu- 
lated, let him consider as follows: — 

1. That all the water above the point of impact, called 
head, acts wholly by percussion, and all below said point, 
called fall, acts wholly by gravity, (see Art. 60:) these 
form the 2d and 3d columns. 

2. That half the head, added to the whole fall, consti- 
tutes the virtual or effectual descent, by Art. 61, w r hich 
is given in the 4th column. 

3. That if the water were permitted to descend freely 
down the circular sheeting, after it passed the point of 
impact, its velocity would be accelerated, by Art. 60, 
so as to be, at the lowest point, equal to the velocity of 
water spouting from under a head equal to the whole de- 
scent; the maximum velocity of this wheel will, conse- 
quently, be compounded of the velocity to suit the head, 
and the acceleration after it passes the point of impact. 
Therefore, to find the velocity of this wheel, I first mul- 
tiply the velocity of the head, in column 5, by ,577, (as 
for undershot mills,) which gives the velocity suitable to 
the head; I then, (by the rule for determining the velo- 
city of overshots,) say, as the velocity of water descending 
21 feet, equal to 37,11 feet per second, is to the velocity 
of the wheel, ,10 feet per second, so is the acceleration of 
velocity, after it passes the point of impact, to the acce- 
lerated velocity of the wheel; and these two velocities 
added, give the velocity of the wheel; which is shown in 
the 6th column. 

4. The velocity of the wheel per second, multiplied bv 
60, and divided by the circumference of the wheel, gives 
the revolutions per minute: see 7th column. 

5. The number of cogs in the cog-wheel, multiplied by 
the number of revolutions, per minute, of the water-wheel, 
and divided by the rounds in the trundle-head, will give 
the number of revolutions of the stone per minute; and 
if we divide by the number of revolutions the stone is to 
have, it gives the rounds in the trundle, and, when frac- 
tions arise, take the nearest whole number; see columns 
8, 9, and 10. 



176 OF BREAST MILLS. [CHAP. IV. 

6. The cubochs of power required to turn the stone, 
by Art. 63, divided by the virtual descent, give the cu- 
bic feet of water required per second ; column 11. 

7. The cubic feet of water, divided by the velocity 
allowed to it in the canal, suppose 1,5 feet per second, 
give the area of a section of the canal: column 12. 

8. If the mill is to be double-geared, take the revolu- 
tions of the wheel from column 7 of this table, and look 
in column 4 of the undershot table, Art. 70, for the num- 
ber of revolutions nearest to it, and against that number 
you have the gearing that will give a 5 feet stone the 
right motion. 



CHAP. IV.] 



OF BREAST MILLS. 



177 



THE MILL-WRIGHT'S TABLE 



BREAST MILLS. 

Calculated for a water-wheel fifteen feet, and stones five feet diameter: the water 
being shot on the direction of a tangent, to the circumference of the wheel. 



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feet. 


feet, i feet. 

1 


feet. 


No. 


No. 


No. 


CU. ft. 


sup. ft. 


6 


1.5 


3.7517.13 


10.61 


13.5 


112 


15 


100.829.8 


19.25 


7 


5. 


2. 


4.5 18. 


11.3 


14.4 


112 


16 


100.8 24.83 


16.55 


8 


5.5 


0.5 


5.2548.99 


12-07 


15.3 


104 


16 


99.421.29 


14.19 


9 


5.9 


3.1 


6.0519.48 


12.53 


16. 


104 


16 


102.7,18.45 


12.3 


10 


6.2 


3.8 


6.9 20.16 


13.07 


16.6 


96 


16 


^99.616.2 


10.8 


11 


6.5 


-1,5 


7.7520.64 


33.53 


17. 


96 


16 


102. 14.42 


9.61 


12 


6.8 


5.3 


8. 721.11 


14.03 


17.81 


96 


17 


100.512.73 


8.49 


13 


6.8 


6.2 


9. 621.11 


14.35 


18.28 


96 


18 


97.511.63 


7.75 


14 


6.9 


7.1 


10.5521.3 


14.41 


18.35 


96 


18 


97.810.59 


7.06 


15 


7. 


8. 


11.5 21.13 


14.76 


18.56 


96 


18 


98.4 9.72 


6.48 


1 


2 


3 


4 5 


6 


7 


8 


9 


10 11 


12 



12 



178 OF BREAST MILLS. [CHAP. IV. 

Use of the Table for Breast-Mills. 

Having a seat with above 6 feet fall, but not enough 
for an overshot mill, and the water being scarce, so that 
you wish to make the best use of it, should lead you to 
the choice of a breast mill. 

Cast off about 1 foot for fall in the tail-race below the 
bottom of the wheel, if much subject to back water, and 
suppose you have then 9 feet total descent; look for 9 
feet in the first column of the table, and against it you 
have it divided into 5,9 feet head above, and 3,1 feet 
fall below, the point of impact, which is the highest point 
that the water can be fairly struck on the wheel : leaving 
the head 3 feet deep above 'the shute; which is equal to 
6,5 feet virtual or effective descent; the velocity of the 
water striking the wheel will be 18,99 feet; and the ve- 
locity of the wheel 12,07 feet per second; it will revolve 
16 times in a minute; and, if single-geared, 104 cogs and 
16 rounds, gives the stone 99,4 revolutions in a minute, 
requiring 21,29 cubic feet of water per second; the area 
of a section of the canal must be 14,19 feet, or about 3 
fqet deep, and 5 feet wide. If the stones be of any other 
size, it is easy to proportion the gearing to give them 
any required number of revolutions.* 

If you wish to proportion the size of the stones to the 
power of your seat, multiply the cubic feet of water 
your stream affords per second, by the virtual descent in 
column 4, and that product is the power in cubochs; 
then look in the table, in Art. 63, for the size of the 
stone that most nearly suits that power. 

For instance, suppose your stream afford 14 cubic feet 
of water per second, then 14 multiplied by 6,05 feet vir- 
tual descent, produce 84,7 cubochs of power; which in 
the table in Art. 63, comes nearest to 4,5 feet for the di- 
ameter of the stones : but by the rules laid down in Art. 
63, the size may be found more exactly. 

* The mill-wright will do well to examine with attention the article in the ap- 
pendix, written by the late W. ParZ-j'w.a practical and scientific workman, whose 
suggestions are of the utmost importance, as they may lead to the correction of 
errors, which the editor is assured, from his own observations, are almost univer- 
s&\, the too great velocity, and the too little capacity of water wheels. 



CHAP. IV.] OF BREAST MILLS. 179 

Six cubochs of power are required to every superfi- 
cial foot of the stones. 



article 73. 

V 

OF OVERSHOT MILLS. 

Fig. 33, Plate IV., represents an overshot wheel: the 
water is laid on at the top, so that the upper part of the co- 
lumn will be in the direction of a tangent, with the cir- 
cumference of the wheel, but so that all the water may 
strike within the circle of the wheel. 

The gate is drawn about 30 inches behind the perpen- 
dicular line from the centre of the wheel, and the point 
at the shute ends at said perpendicular with a direction 
a little downwards, which gives the water a little velo- 
city downwards to follow the wheel; for if it be directed 
horizontally, the head will give it no velocity downwards, 
and if the head be great, the parabolic curve, which the 
spouting water forms, will extend beyond the outside of 
the circle of the wheel, and it will incline to fly over. 
See Art. 44 and 60. 

The head above the wheel acts by percussion, as on 
an undershot wheel, and we have shown, Art. 43, that 
the head should be such as to give to the water a velo- 
city of 3, for 2 of the wheel. After the water strikes 
the wheel, it acts by gravity; therefore, to calculate the 
power, we must take half the head and add it to the fall, 
for the virtual descent, as in breast mills. 

The velocity of overshot wheels is as the square roots 
of their diameters. See Art. 43. 

On these principles, I have calculated the following 
table for overshot wheels; and, in order that the reader 
may understand it fully, let him consider well the follow- 
ing premises: — 

I. That the velocity of the water spouting on the 
wheel must be one and a half times the velocity of the 
wheel, by Art. 43: then, to find the head that will give 
said velocity, say as the square of 16,2 feet per secon I, 
is to 4 feet, the head that gives that velocity, so is tha 



180 OF OVERSHOT MILLS. [CHAP. IV. 

square of the velocity required, to the head that will 
give the velocity sought for; but to this head, so found, 
we must add a little, by conjecture, to overcome the 
friction of the aperture. See Art. 55. 

In this table, I have added to the heads of wheels of 
from 9 to 12 feet diameter ,1 of a foot, and from 12 to 20 
feet I have added one-tenth more, for every foot increase 
of diameter, and from 20 to 30 feet I have added ,05 
more to every foot diameter's increase; which gives a 30 
feet wheel 1,5 feet additional head, while a 9 feet wheel 
has only one-tenth of a foot, to overcome the friction. 
The reason of this great difference will appear when we 
consider that the friction increases as the aperture de- 
creases, and as the velocity increases: still this depends 
much on the form of the gate, for if that be nearly square, 
there will be but little friction; but if very oblong, say 
24 inches by half an inch, then it will be very great. 

The heads thus found, compose the 3d column. 

2. The head, added to the diameter of the wheel, makes 
the total descent, as in column 1. 

3. The velocity of the wheel per second, taken from 
the table in Art. 43, multiplied by 60, and divided by 
the circumference of the wheel, gives the number of re- 
volutions of the wheel per minute; as in column 4. 

4. The number of revolutions of the wheel, per mi- 
nute, multiplied by the number of cogs in all the driving 
wheels successively, and that product divided by the pro- 
duct of all the leading wheels, gives the number of revo- 
lutions of the stone per minute, and is found in column 
9, double gear, for 5 feet stones; and in column 12, sin- 
gle gear, for 6 feet stones. 

5. The cubochs of power required to drive the stone, 
by table in Art. 63, divided by the virtual or effective 
descent, which is half the head added to the fall, or the 
diameter of the wheel, gives the cubic feet of water re- 
quired per second to drive the stone, and is column 13. 

6. The cubic feet required, divided by the velocity 
you intend the water to have in the canal, gives the area 
of a section of the canal. The width multiplied by the 
depth, must always produce this area. See Art. 64. 



CHAP. IV.] OF OVERSHOT MILLS. 181 

7. The number of cogs in the wheel, multiplied by the 
quarters of inches in the pitch, produces the circumfe- 
rence of the pitch circle; which multiplied by 7, and di- 
vided by 22, gives the diameter in quarters of inches, 
which reduced to feet and parts, forms column 15. The 
reader may here at once observe how near the cog-wheel, 
in the single gear, will be to the water ; that is, how near 
it is, in size, to the w r ater-wheel. 



Use of the Table. 

Having with care levelled the seat on which you mean 
to build, and found, that after deducting 1 foot for fall 
below the wheel, and a sufficiency for the sinking of the 
head race, according to its length and size, and having 
a total descent remaining sufficient for an overshot wheel, 
suppose 17 feet; then, on looking in the first column of 
the table, for the descent nearest to it, we find 16,74 feet, 
and against it a wheel 14 feet diameter: head above the 
wheel 2,7 feet; revolutions of the wheel per minute 11, 
17; double gears, to give a 5 feet stone 98,7 revolutions 
per minute; single gears, to give a 6 feet stone 76,6 re- 
volutions per minute ; the cubic feet of water required 
for a 5 feet stone 7,2 feet per second, and the area of a 
section of the canal 5 feet; about 2 feet deep, and 2,5 
feet wide. 

If it be determined to proportion the size of the stones 
exactly to suit the power of the seat, it may be done as 
directed in Art. 63. All the rest can be proportioned 
by the rules by which the table is calculated. 



182 



OF OVERSHOT MILLS. 



[CHAP. IV. 



THE MILL-WRIGHT'S TABLE 

FOR 

OVERSHOT MILLS- 

Calculated for five feet stones, double gear, and six 
feet stones, single gear. 



o 


d 


EC 

CD 


si 


Double gear, 5 
feet stones. 


Single gear 
6 ft. stones. 


Q 

s 


> 


9 \ 


tal descent of the wa 
this table made to si 
of the wheel and head 


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feet. 








44 


16 


r 




11 


78. 


•-I 


>— 03 


■H- S. 






21 


102.9 


60 


cub.ft. 


sup. ft. 


feet, inches. 


10.51 


9 


1.51 


14.3 


54 


11.46 


11.46 


6:9 0-4 12-22 


11.74 


10 


1.74 


13. 


54 


21 


48 


18 


98. 


60 


10 


78. 


10.3 


10.3 




12.9-1 


11 


1.94 


12.6 


60 


21 


48 


18 


96. 


66 


11 


75.6 


9.34 


9.34 


7:5 1-4 


14.2 


12 


2.2 


12. 


66 


23 


48 


17 


97. 


66 


10 


79.2 


8.53 


8.53 




15.47 


13 


2.47 


11.54 


66 


21 


48 


L7 


99.3 


84 


12 


80.7 


7.92 


7.92 


9:5 1-2 


16.74 


14 


2.74 


11.17 


72 


•23 


48 


17 


98.7 


96 


14 


76.6 


7.2 


7.2 


10:9 3-4 6-22 


17.99 


15 


2.99 


10.78 


78 


23 


4 s 


18 


98.3 


96 


13 


81.9 


6.77 


6.77 




19.28 


16 


3.28 


10.4 


78 


23'48 


17 


99.5 


120 


16 


76. 


6.4 


6.4 


13:6 1-4 2-22 


20.5 


17 


3.5 


10.1 


78 


2148 


18 


96.6 


120 


15 


80.8 


6. 


6. 




21.8 


IS 


3.8 


9.8 


84 


24|48 


17 


97. 


128 


16 


78.4 


5.56 


5.56 


14:5 0-4 8-22 


23.03 


li) 


4.03 


9.54 


84 


23 


48 


17 


98.3 


128 


15 


81.4 


5.32 


5.32 




24.34 


20 


4.34 


9.3 


88 


2:', 


48 


17 


100. 


128 


15 


79.3 


5.04 


5.04 




25.54 


21 


4.54 


9.1 


88 


23 


48 


17 


98.3 


128 


15 


77.6 


4.81 


4.81 




26.86 


22 


4.8(5 


8.9 


96 


■24 


18 


17 


100.5 


128 


14 


81.4 


4.57 


4.57 




27.99 


23 


4.99 


8.7 


96 


25 


54 


18 


100.2 








4.34 


4.34 




29 27 


24 


5.27 


8.5 


96 


25 


54 


17 


103. 








4.19 


4.19 




30.45 


25 


5.45 


8.3 


96 


25 


54 


17 


101. 








4. 


4. 




31.57 


26 


5.57 


8.19 


96 


25 


51 


17 


99.6 








3.82 


3.82 




32.77 


27 


5.77 


8.03 


104 


25 


54 


18 


100.2 








3.7 


3.7 




33.96 


28 


5.96 


7.93 


104 


25 


54 


18 


99. 








3.6 


36 




35.15 


29 


6.15 


7.75 


112 


2(i 


54 


18 


100.1 








3.4 


3.4 




36.4 


30 

2 


6.4 


7.63 


112 


20 


54 
7 


IS 
8 


9 8.6 
9 


To" 






3.36 


3.36 




1 


3 


4 


5 





11 


12 


13 


14 


15 



CHAP. IV.] OF OVERSHOT MILLS. 183 



Observations on the Tables. 

1. It appears that single gearing does not well suit this 
construction; because, where the water wheels are low, 
their motion is so slow that the cog-wheels, (if made 
large enough to giye sufficient motion to the stone, with- 
out having the trundle too small, see Art. 23,) will touch 
the water. And again, when the water wheels are above 
20 feet high, the cog-wheels require to be so high, in 
order to give motion to the stone without having the 
trundle too small, that they become unwieldy; the husk 
also is too high, and the spindle so short as to be incon- 
venient. Single gearing, therefore, seems to suit over- 
shot wheels only where their diameter is between 12 and 
18 feet, and even then the water wheel will have to run 
rather too fast, or the trundle be too small, and the stones 
should be, at least, 6 feet in diameter. 

2. I have, in the preceding tables, supposed the wa- 
ter to pass along the canal with 1,5 feet velocity per se- 
cond; but being of opinion that 1 foot per second is near- 
er the proper motion, that is, about 20 yards per minute, 
the cubic feet required per second, will, in this case, be 
the area of a section of the canal, as given in column 14 
of this table. 

3. Although I have calculated this table for the velo- 
cities of the wheels to vary as the square roots of their 
diameters, which makes a 30 feet wheel move 11,99 feet 
per second, and a 12 feet wheel to move 7,57 feet per se- 
cond, yet they will do to have equal velocity and head, 
which is the common practice among mill-wrights. But, 
for the reasons I have mentioned in Art. 43, I prefer 
giving them the velocity and head assigned in the table, 
in order to obtain steady motion. 

4. Many have been deceived, by observing the ex- 
ceedingly slow and steady motion of some very high 
overshot wheels, working forge or furnace bellows, con- 
cluding therefrom, that they will work as steadily with a 
very slow, as with any quicker motion, not considering, 
perhaps, that it is the principle of the bellows that re- 



184 OF OVERSHOT MILLS. [CHAP. IV. 

gulates the motion of the wheel, which is different from 
any other resistance, for it soon becomes perfectly equa- 
ble, therefore the motion will be uniform, which is not 
the case with mills of any kind. 

5. An opinion is sometimes entertained, that water is 
not well applied by an overshot wheel, because, it is said, 
those buckets which nearly approach a line drawn per- 
pendicularly through the centre, either above or below, 
act on too short a lever. To correct this erroneous idea, 
I have divided the fall of the overshot wheel, fig. 33, 
Plate IV., into feet, shown by dotted lines. Now, by 
Art. 53 and 54, every cubic foot of water on the wheel 
produces an equal quantity of power in descending each 
perpendicular foot, called a cuboch of power; and that 
because where the lever is shortest, the greatest quan- 
tity of water is contained within the foot perpendicular; 
or, in other words, each cubic foot of water is a much 
longer time, and passes a greater distance, in descending 
a perpendicular foot, than where the lever is longest ; 
this exactly compensates for the deficiency in the length 
of lever. See this demonstrated, Art. 54. It is true, 
that the effect of the lower foot is, in practice, entirely 
lost, by the running of the water out of the buckets. 



Of Mills moved by Reaction. 

We have now treated of the four different kinds of 
mills that are in general use. There is another, the in- 
vention of, or rather an improvement by, the late in- 
genious James Rumsey, which moves by the reaction 
of water.* 

* This is sometimes known by the name of Barker's mill ; several of which 
have been built in different places; but it is believed that they have all been aban- 
doned, as they have not in practice answered the expectations which had been 
entertained respecting them. A modification of this mode of applying the power 
of water has, of late years, been extensively used in the United States, and been 
made the subject of several patents. These wheels will be noticed in the appen- 
dix. — Editor. 






CHAP. V.] RULES AND CALCULATIONS. 185 



CHAPTER V. 

ARTICLE 74. 
RULES AND CALCULATIONS. 

The fundamental principle, on which are founded all 
rules for calculating the motion produced by a combina- 
tion of wheels, and for calculating the number of cogs to 
be put in them, to produce any motion that is required, 
has been given in Art. 20; and is as follows: — 

If the revolutions that the first moving wheels make 
in a minute be multiplied by the number of cogs in all 
the driving wheels successively, and the product noted ; 
and the revolutions of the last leading wheel be multi- 
plied by the number of cogs in all the leading wheels 
successively, and the product noted; these products will 
be equal in all possible cases. Hence, we deduce the 
following simple rules: — 

1st. For finding the motion of the mill-stone; the re- 
volutions of the water-wheel, and the cogs in the wheels, 
being given: — 

RULE. 

Multiply the revolutions of the water-wheel per mi- 
nute, by the number of cogs in all the driving wheels 
successively, and note the product; and multiply the 
number of cogs or rounds in all the leading wheels suc- 
cessively, and note the product; then divide the first 
product by the last, and the quotient is the number of 
revolutions of the stone per minute. 

EXAMPLE. 

Given the revolutions of the water-wheel per 

minute, --__-- 10,4 

No. of cogs in the master cog-wheel - 78 > j^ . 
No. of do. in the counter cog-wheel - 48 £ 
No. of rounds in the wallower - - 23 ) j , 
No. of do. in the trundle - - - 1? 5 



186 RULES AND CALCULATIONS. [CHAP. V. 

Then 10,4, the revolutions of the water-wheel, multi- 
plied by 78, the cogs in the master-wheel, and 48, the 
cogs in the counter-wheel, are equal to 38937,6; and 23 
rounds in the wallower, multiplied by 17 rounds in the 
trundle, are equal to 391, by which we divide 38937,6, 
and it gives 99,5, the revolutions of the stone per minute; 
which are the calculations for a 16 feet wheel, in the 
overshot table. 

2d. For finding the number of cogs to be put in the 
wheels, to produce any number of revolutions required 
to the mill-stone, or to any wheel. 

RULE. 

Take any suitable number of cogs for all the wheels 
except one; then multiply the revolutions of the first 
mover per minute, by all the drivers, except the one 
wanting, (if it be a driver,) and the revolutions of the 
wheel required, by all the leaders, and divide the great- 
est product by the least, and it will give the number of cogs 
required in the omitted wheel, to produce the desired re- 
volutions. 

^Note. If any of the wheels be for straps, take their di- 
ameters in inches and parts, and multiply and divide with 
them, as with the cogs. 

EXAMPLE. 

Given, the revolutions of the water-wheel 10, 

And the cogs in the master-wheel - 78 ) p. • 
Ditto in the counter wheel - - - 48 £ 
Rounds in the wallower - - - 23 

The number of the trundle is required, to give the 
stone 99 revolutions. 

Then 10,4, multiplied by 78 and 48, is equal to 
38937,6; and 99, multiplied by 23, is equal to 2277, by 
which divide 38937,6, and it gives 16,66; instead of 
which, I take the nearest whole number, 17, for the 
rounds in the trundle, and find, by rule 1st, that it pro- 
duces 99,5 revolutions as required. 

For the exercise of the inexperienced, I have con- 
structed fig. 7, Plate XI. ; which I call the circle of mo- 



CHAP. V.] RULES AND CALCULATIONS. 187 

tion, and which serves to prove the fundamental princi- 
ple on which the rules are founded; the first shaft be- 



ing, also, 


the last or tl 


lie circl 


e. 






A is 


a cog-wheel of 20 i 


cogs, 


and is 


a driver. 


B 


do. 


24 




- 


leader. 


C 


do. 


24 




- 


driver. 


D 


do. 


30 




- 


leader. 


E 


do. 


25 




- 


driver. 


F 


do. 


30 




- 


leader. 


G 


do. 


36 




- 


driver. 


H 


do. 


20 




- 


leader. 



But if we trace the circle the backward way, the lead- 
ers become drivers. 

I is a strap- wheel 14| inches diameter, driver. 
K do. 30 do. - leader. 

L cog-wheel 12 cogs. - driver. 

M do. 29 do. - leader. 

MOTION OF THE SHAFTS. 

The upright shaft, and first driver, AH 36 revs, in a min. 

BC 30 do. 
DE 24 do. 
FG 20 do. 
HA 36 do. 

M 4 do., which is 

the shaft of a hopper-boy. 

If this circle be not so formed, as to give the first and 

last shafts (which are here the same) exactly the same 

motion, one of the shafts must break as soon as they are 

put in motion. 

The learner may exercise the rules on this circle, un- 
til he can form a similar circle of his own ; and then he 
need never be afraid to undertake to calculate any other 
combination of motion. 

I omit showing the work for finding the motion of the 
several shafts in this circle, and the wheels to produce 
said motion ; but leave it for the practice of the learner, 
in the application of the foregoing rules. 



188 RULES AND CALCULATIONS. [CHAP. V. 

EXAMPLES. 

1st. Given, the first mover AH 36 revolutions per 
minute, and first driver A 20 cogs, leader B 24; re- 
quired, the revolutions of shaft BC. Answer, 30 revolu- 
tions per minute. 

2dly. Given, first mover 36 revolutions per minute, dri- 
vers 20 — 24 — 25, and leaders 24 — 30 — 30; required the 
revolutions of the last leader. Answer, 20 revolutions 
per minute. 

3dly. Given, first mover 20 revolutions per minute, 
and first driver, strap-wheel, 14| inches, cog-wheel 12, 
and leader, strap-wheel, 30 inches, cog-wheel 29; re- 
quired, the revolutions of the last leader, or last shaft. 
Answer, 4 revolutions. 

4thly. Given, first mover 36 revolutions, driver A 20, 
C 24, leader B 24, D 30 ; required the number of lead- 
er F, to produce 20 revolutions per minute. Answer 30 
cogs. 

5thly. Given, first mover 36 revolutions per minute, 
driver A 20, C 24, E 25, driver pulley 14£ inches dia- 
meter, L 12, and leader B 24, D 30, F 30^ M 29; re- 
quired the diameter of the strap-wheel K, to give the 
shaft 4, four revolutions per minute. Answer, 30 inches 
diameter. 

The learner may, for exercise, work the above ques- 
tions, and every other that he can propose on the circle. 



article 75. 

The following are the proportions for finding the cir- 
cumference of a circle, its diameter being given, or the 
diameter by the given circumference; namely: — 

As 1 is to 3,1416, so is the diameter to the circumfe- 
rence; and as 3,1416 is to 1, so is the circumference to 
the diameter: Or, as 7 is to 22, so is the diameter to the 
circumference; and as 22 is to 7, so is the circumference 
to the diameter. The last proportion makes the diame- 
ter a little too large; it, therefore, suits mill-wrights best 



CHAP. V.] RULES AND CALCULATIONS. 189 

for finding the pitch circle; because the sum of the dis- 
tances, from centre to centre, of all the cogs in a wheel, 
makes the circle too short, especially where the number 
of cogs is few, because the distance is taken in straight 
lines, instead of on the circle. In a wheel of 6 cogs only, 
the circle will be so much too short, as to give the dia- 
meter ~ parts of the pitch or distance of the cogs too 
short. Hence, we deduce the following 

RULES FOR FINDING THE PITCH CIRCLE. 

Multiply the number of cogs in the wheel, by the 
quarters of inches in the pitch, and that product by 7, 
and divide by 22, and the quotient is the diameter in 
quarters of inches, which is to be reduced to feet. 

EXAMPLE. 

Given, 84 cogs 4-i inches pitch; required the diameter 
of the pitch circle. 

Then, by the rule, 84 multiplied by 18, and by 7, is 
equal to 10584; which, divided by 22, is equal to 481 ¥ \ 
quarter inches, equal to 10 feet ~\ inches, for the diame- 
ter of the pitch circle required. 



article 76. 

A true and expeditious method of finding the diameter 
of the pitch circle, is to find it in measures of the pitch 
itself that you use. 

RULE. 

Multiply the number of cogs by 7, and divide by 22, 
and you have the diameter of the pitch circle, in measures 
of the pitch, and the 22d parts of said pitch. 

EXAMPLE. 

Given, 78 cogs; required the diameter of the pitch 
circle. Then, by the rule, 



190 RULES AND CALCULATIONS. [CHAP. V. 

78 

7 



22)546(24i| ( Measures of the pitch for the diameter 
44 ( of the circle required. 



106 

88 



18 

Half of which diameter, 12^ of the pitch, is the radius, 
or half diameter, by which the circle is to be swept. 

To use this rule, set a pair of compasses to the pitch, 
and screw them fast, so as not to be altered until the 
wheel is pitched: divide the pitch into 22 equal parts; 
then step 12 steps, on a straight line with the pitch com- 
passes, and 9 of these equal parts of the pitch, make the 
radius that is to describe the circle. 

To save the trouble of dividing the pitch for every 
wheel, the workman may mark the different pitch which 
he commonly uses, on the edge of his two-foot rule, (or 
make a little rule for the purpose,) and carefully divide 
them there, where they will always be ready for use. 
See Plate IV. fig. 35. 

By these rules, I have calculated the following table 
of the radii of pitch circles of the different wheels com- 
monly used, from 6 to 136 cogs. 



CHAP. V.] 



RULES AND CALCULATIONS. 



191 



A TABLE 

OF THE 

PITCH CIRCLES OF THE COG-WHEELS, 

COMMONLY USED, 
From 6 to 136 cogs, "both in measures of the pitch, and in feet, inches, and parts. 



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Radius of th 
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pitch. 


Radius of th 
of the whee 
column tal 
inches, quai 
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the pitch is 
large gears, 


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34 


5 9 


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5 12 1-2 


1:11:2:14 1-22: 1:0: 5 


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36 


5 16 


2: 0:1: 8 2: 1:3: 2 


10 


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37 


5 19 1-2 2: 1:0: 1 1-2,2: 2:1:21 


11 


1 


17.1 


4:1:17 




38 


6 1 2: 1:2:17 2: 3:0:10 


12 


1 


20.5 


4:3: 5 




39 


6 4 1-2 2: 2:1:10 1-2 2: 3:3:15 


13 2 


1.9 


5:0:17 




40 


6 8 


2: 3:0: 4 


2: 4:2:12 


14 1 2 


5.3 


5:2: 8 




42 


6 15 


2: 4:1:13 


2: 6:0: 6 


15 1 2 


8.8 


5:3:20 




44 


7 


2: 5:3: 


2: 7:2: 


16' 2 


12.2 


6:1:11 




48 


7 14 


2: 8:1:18 


2:10:1:10 


17 


2 


15.7 


6:3:2 




52 


8 4 


2: 11:0:14 


3: 1:0:20 


18 


2 


191 


7:0:15 




54 


8 11 


3: 0:2. 1 


3: 2:2:14 


19 


3 


0.6 


7:2: 6 




56 


8 20 


3: 1:3:10 


3: 4:0. 8 


,20 


3 


4.1 


7:3:18 




60 


9 13 


3: 4:2: 6 


3: 6:3:18 


21 


3 


7.5 


8:1: 9 




66 


10 11 


3: 8:2:11 


3:11:1: 


22 


3 


11. 


8:3: 




72 


11 10 


4: 0:2:16 


4: 3:2: 4 


23 


3 


14.5 


9:0:13 




78 


12 9 


4: 4:2:21 


4: 7:3: 8 


h 


3 


18. 


9:2:4 




81 


13 8 


4: 8:3: 4 


5: 0.0:12 


25 


3 


21.5 


9:3:17 




8814 


4: 11:2: 


5: 3:0: 


26 


4 


3. 


10:1: 8 




9014 7 


5: 0:3: 9 


5: 4:1:16 


27 


4 


6.5 


10:2:21 




9615 6 


5: 4:3:14 


5: 8:2:20 


,28 


1 4 


10. 


11:0:12 




104 16 13 


5: 10: 1: 6 


6: 2:1:18 


29 1 4 


13.5 


11:2: 3 




11217 18 


6: 3:2:20 


6: 8:0:16 


'SO 4 


17. 


11:3:16 




120 19 2 


6: 9:0:12 


7: 1:3:14 


3l| 4 


20.5 


12:1: 7 




1282) 8 


7: 2:2: 4 


7: 7:2:12 


3-2 


6 


.2 


12:2:20 




13621 14 

l 


7: 7:3:18 


8: 1:1:10 


1 




2 


1 3 




U ' 5 | 


1 



192 RULES AND CALCULATIONS. [cHAP. V. 

Use of the foregoing Table. 

Suppose you are making a cog-wheel with 66 cogs; 
look for the number in the 1st or 4th column, and against 
it, in the 2d or 5th column, you find 10, 11 ; that is, 10 
steps of the pitch (you use) in a straight line, and 11 of 
22 equal parts of said pitch added, make the radius that 
is to describe the pitch circle. 

The 3d, 6th and 7th columns, contain the radius in 
feet, inches, quarters and 22 parts of a quarter; which 
may be made use of in roughing out timber, and fixing 
the centres that the wheels are to run in, so that they 
may gear to the right depth; but on account of the dif- 
ference in the parts of the s'ame scales or rules, and the 
difficulty of setting the compasses exactly, they can never 
be true enough for the pitch circles. 

RULE COMMONLY PRACTISED. 

Divide the pitch into 11 equal parts, and take in your 
compasses 7 of those parts, and step, on a straight line, 
counting four cogs for every step, until you come up to 
the number in your wheel; if there be an odd one at 
last, take | of a step — if two be left, take \ of a step — ■ 
if 3 be left, take \ of a step, for them; and these steps, 
added, make the radius or sweep-staff of the pitch cir- 
cle; but on account of the difficulty of making these di- 
visions sufficiently exact, there is little truth in this 
rule — and where the number of cogs is few, it will make 
the diameter too short, for the reasons formerly men- 
tioned. 

The following geometrical rule is more true, and in 
some instances, more convenient. 

RULE. 

Draw the line AB, plate IV. fig. 34, and draw the line 
0,22 at random; then take the pitch in your compasses, 
and beginning at the point 22, step 11 steps towards A, 
and 3| steps to point X, towards O, draw the line AC 
through the point X; draw the line DC parallel to AB, 



CHAP. V.] RULES AND CALCULATIONS. 1 93 

and, without having altered your compasses, begin at 
point O, and step both ways, as you did on AB, then, 
from the respective points, draw the cross lines parallel 
to 0,22 ; and the distance from the point, where they 
cross the line AC, to the line AB, will be the radius of 
the pitch circles for the number of cogs respectively, as 
in the figure. If the number of cogs be odd, say 21, the 
radius will be between 20 and 22. 

This will also give the diameter too short, if the wheels 
have but few cogs; but where the number of cogs is 
above twenty, the error is imperceptible. 

All these rules are founded on the proportion, that, as 
22 is to 7, so is the circumference to the diameter. 

article 77. 

CONTENTS OF GARNERS, HOPPERS, &C. IN BUSHELS. 

A Table of English Dry Measure. 

The bushel contains 
2150.4 solid inches. 
Therefore, to mea- 
sure the contents of 
any garner, take the 
following 

RULE. 

Multiply its length in inches, by its breadth in inches, 
and that product by its height in inches, and divide the 
last product by 2150,4 and it will give the bushels it con- 
tains. 

But, to shorten the work decimally; because 2150,4 
solid inches, make 1,244 solid feet, multiply the length, 
breadth, and height, in feet, and decimal parts of a foot, 
by each other, and divide by 1,244, and it will give the 
contents in bushels. 

EXAMPLE. 

Given, a garner 6,25 feet long, 3,5 feet wide, 10,5 
feet high; required its contents in bushels. Then, 0,25 
^13 



Solid "^\^ 
Inches. ^~^\^ 


3.36 


Pint. ~\^ 


268.8 | 


8 | Gall. ^\ 


537.6 


16 | 2 | Peck. \^ 


2150.4 


64 | 8 | 4 | Bushel. ^\ 



194 RULES AND CALCULATIONS. [cHAP. V. 

multiply by 3,5 and 10,5 is equal to 229,687; which, di- 
vide by 1,244, gives 184 bushels and 6 tenths. 

To find the contents of a hopper, take the following 

RULE. 

Multiply the length by the width at the top, and that 
product by one-third of the depth, measuring to the very 
point, and divide by the contents of a bushel, either in 
inches or decimals, and the quotient will be the contents 
in bushels. 

EXAMPLE. 

Given, a hopper, 42 inches square at the top, and 24 
inches deep; required, the contents in bushels. 

Then 42 multiplied by 42, and that product by 8, is 
equal to 14112 solid inches: which, divided by 2150,4, 
the solid inches in a bushel, gives 6,56 bushels, or a little 
more than 6§ bushels. 

To make a garner to hold any given quantity, having 
two of its sides given, pursue the following 

RULE. 

'Multiply the contents of 1 bushel by the number of 
bushels the garner is to hold; then multiply the given 
sides into each other, and divide the first by the last pro- 
duct, and the quotient will be the side wanted, in the same 
measure by which you have wrought in. 

EXAMPLE. 

Given, two sides of a garner 6,25 by 10, Of t: re- 
quired, the other side, to hold 184,6 bushels. 

Then, 1,244 multiplied by 184,6 is equal to 229,642; 
which, divided by the product of the two sides, 65,625, 
the quotient is 3,5 feet for the side wanted. 

To make a hopper to hold any given quantity, having 
the depth given. 

RULE. 

Divide the inches contained in the bushels it is to hold, 
by l-3d the depth in inches; and the quotient will be the 
square of one of the sides, at the top in inches. 



CHAP. VI.] OF SPUR GEARS. 195 

Given, the depth 24 inches; required, the sides to hold 
6,56 bushels. 

Then 6,56 multiplied by 2150,4 equal to 14107,624; 
which, divided by 8, gives 1764, the square root of which 
is 42 inches; which is the length of the sides of the hop- 
per wanted. 



CHAPTER VI. 

ARTICLE 78. 
OF THE DIFFERENT KINDS OF GEARS, AND FORMS OF COGS. 

In order to conceive a just idea of the most suitable 
form or shape of cogs in cog-wheels, we must consider 
that they describe, with respect to the pitch circles, a 
figure called an Epicycloid. 

And when one wheel works in cogs set in a straight 
line, such as the carriage of a saw-mill, the cogs or rounds 
moving out and in, form a curve called a Cycloid. 

To describe this figure, let us suppose the large circle 
in Plate V., fig. 37, to move on the straight line from O 
to A ; then the point O, in its periphery, will describe the 
arch ODA, which is called a Cycloid ; and by the way in 
which the curve joins the line, we may conceive what 
should be the form of the point of the cog. 

Again, suppose the small circle to run round the large 
one; then the point o, in the small circle, will describe 
the arch O b C, called an Epicycloid; by which we may 
conceive what should be the form of the point of the cogs. 
But in common practice, we genera ly let the cogs ex- 
tend but a short distance past the pitch circle; so that 
their precise form is not so important. 

article 79. 

OF SPUR GEARS. 

The principle of spur gears, is that of two cylinders 
rolling on each other, with their shafts or axes truly pa- 



196 OF SPUR GEARS. [CHAP. VI. 

rallel. Here the touching parts move with equal velo- 
city, and have, therefore, but little friction; but to pre- 
vent these cylinders from slipping, we are obliged to in- 
dent, or to set cogs in them. 

It appears to me that, in this kind of gear, the pitch of 
the driving wheel should be a little larger than that of 
the leading wheel, for the following reasons: — 

1. If there is to be any slipping, it will be much easier 
for the driver to slip a little past the leader, than for the 
cogs to have to force the leader a little before the driver ; 
which would be very hard on them. 

2. If the cogs should bend any, by the stress of the 
work, as they assuredly do, this will cause those that are 
coming into gear to touch too soon, and rub hard at en- 
tering. 

3. It is much better for cogs to rub hard as they are 
going out of gear, than as they are coming in; because 
then they work with the grain of the wood; whereas, at 
entering they work against it, and would wear much 
faster. 

The advantage of this kind of gear is, that we can 
make the cogs as wide as we please, so that their bearing 
may be so large that they will not cut, but only polish 
each other, and wear smooth ; therefore, they will last a 
long time. 

Their disadvantages are, 

1st. That if the wheels be of different sizes, and the 
pitch circles are not made to meet exactly, they will not 
run smoothly. And, 

2dly. We cannot, conveniently, change the direction 
of the shafts. 

Fig. 38, Plate V. shows two spur-wheels working into 
each other; the dotted lines show the pitch circles, which 
must always meet exactry. The ends of the cogs are 
made circular, as is commonly done; but if they were 
made true epicycloids, adapted to the size of the wheels, 
they would work with less friction, and, consequently, be 
much better. 






CHAP. VI.] OF FACE GEARS. 197 

Fig. 39, is a spur and face wheel, or wallower, whose 
pitch circles should always meet exactly. 

The rule for describing the sides of the cogs, so as 
nearly to approach the figure of an epicycloid, is as fol- 
lows; namely: Describe a circle a little inside of the pitch 
circle, for the point of your compasses to be set in, so as 
to describe the sides of the cogs, (as the four cogs at A, 
Plate V. fig. 38 — 39,) as near as you can to the curve of 
the epicycloid that is formed by the little wheel moving 
round the great one ; the greater the difference between 
the great and small wheels, the greater distance must 
this circle be within the pitch circle: in doing this pro- 
perly, much will depend upon the judgment of the work- 
man.* 



article 80. 



OF FACE GEARS. 



The principle of face gears is that of two cylinders 
rolling with the side of one on the end of the other, 
their axes being at right angles. Here, the greater the 



* The following is Mr. Charles Taylor's rule for ascertaining the true cycloid- 
ical or epicycloidical form for the point of cogs: — 

Make a segment of the pitch circle of each wheel, which gear into each other; 
fasten one to a plain surface, and roll the other round it, as shown, Plate V. fig. 
37, and, with a point in the moveable segment, describe the epicycloid o b c; set 
off at the end o one-fourth part of the pitch for the length of the cog outside of the 
pitch circle. Then fix the compasses at such an opening, that with one leg there- 
of in a certain point, (to be found by repeated trials,) the other leg will trace the 
epicycloid from the pitch circle to the end of the cog : preserve the set of the com- 
passes, and through the point where the fixed leg stood, sweep a circle from the 
centre of the wheel, in which set one point of the compasses to describe the point 
of all the cogs of that wheel whose segment was made fast to the plane. 

If the wheels be bevel gear, this rule may be used to find the true form of both 
the outer and inner ends of the cogs, especially if the cogs be long, as the epicy- 
cloid is different in different circles. In making cast iron wheels, it is absolutely 
necessary to attend to forming the cogs in the true epicycloidical figure, without, 
which they will grind and wear rapidly. 

The same rule serves for ascertaining the cycloidical form of a right line of 
cogs, such as those of a saw-mill carriage, &c, or of cogs set inside of a circle or 
hollow cone. Where a wheel works within a wheel, the cogs require a very dif- 
ferent shape. 



198 OF FACE GEARS. [CHAP. VI. 

bearing, and the less the diameter of the wheels, the 
greater will be the friction ; because the touching parts 
move with different velocities — therefore the friction will 
be great. 

The advantages of this kind of gear are, 

1st. Their cogs stand parallel to each other; there- 
fore, moving them a little out of or in gear, does not alter 
the pitch of the bearing parts of the cogs, and they will 
run smoother than spur gears, when their centres are out 
of place. 

2dly. They serve for changing the direction of the 
shafts. 

Their disadvantages are, 

1st. The smallness of the bearing, so that they wear 
out very fast.* 

2dly. Their great friction and rubbing of parts. 

The cogs for small wheels are generally round, and 
put in with round shanks. Great care should be taken 
in boring the holes for the cogs, with a machine, to direct 
the auger straight, that the distance of the cogs may be 
equal, without dressing. And all the holes of all the 
small wheels in a mill should be bored with one auger, 
a»d made of one pitch; then the miller may keep by him 
a quantity of cogs ready turned to a gauge, to suit the 
auger; and when any fail, he can put in new ones, with- 
out much loss of time. 

Fig. 40, Plate V. represents a face cog-wheel working 
into a trundle; showing the necessity of having the cor- 
ners of the sides of the cogs sniped, or worked off in a 
cycloidal form, to give liberty for the rounds to enter be- 
tween the cogs, and pass out again freely. To describe 
the sides of the cogs of the right shape to meet the rounds 
when they get fairly into gear; as at c, there must be a 
circle described on the ends of the cogs, a little outside 
of the pitch circle, for the point of the compasses to be 
set in, to describe the ends of the cogs; for, if the 
point be set in the pitch circle, it will leave the inner 

* If the beavins; of the cogs be small, and the stress so great that they cut one 
another, they will wear exceedingly fast; but if it be so large, and the stress so 
light, that they only polish one another, they will last very long. 



CHAP. VI.] OF BEVEL GEARS. 199 

corners too full, and make the outer ones too scant. 
The middle of the cogs is to be left straight, or nearly so, 
from bottom to top, and the side nearly flat, at the dis- 
tance of half the diameter of the round, from the end, the 
corners only being worked off to make the ends of the 
shape in the figure; because, when the cog comes fully 
into gear, as at c, the chief stress is there, and there the 
bearing should be as large as possible. The smaller the 
cog-wheel, the larger the trundle, and the wider the cogs, 
the more will the corners require to be worked off. Sup- 
pose the cog-wheel to turn from 40 to b, the cog 40, as it 
enters, will bear on the lower corner, unless it be suffi- 
ciently worked off; when it comes to c, it will be fully in 
gear: and if the pitch of the cog-wheel be a little larger 
than that of the trundle, the cog a will bear as it goes out, 
and let c fairly enter before it begins to bear. 

Suppose the plumb line A B to hang directly to the 
centre of the cog-wheel, the spindle isV by many mill- 
wrights, set a little before the line or centre, that the 
working round, or stave, of the trundle may be fair with 
said line, and meet the cog fairly as it comes to bear; by 
this means, also, the cogs enter with less, and go out with 
more friction. Whether there be any real advantage in 
thus setting the spindle foot before the centre plumb line, 
does not seem to be determined. 



article 81. 

OF BEVEL GEARS. 

The principle of bevel gears, is that of two cones roll- 
ing on the surface of each other, their vertexes meeting 
in a point, as at A, fig. 41, Plate V. Here the touching 
surfaces move with equal velocities in every part of the 
cones ; therefore, there is but little friction. These cones, 
when indented, or fluted, with teeth diverging from the 
vertex to the base, to prevent them from slipping, be- 
come bevel gear; and as these teeth are very small at the 



200 OF BEVEL GEARS. [CHAP. VI. 

point or vertex of the cone, they may be cut off 2 or 3 
inches from the base, as 19 and 25, at B; they then have 
the appearance of wheels. 

To make these wheels a suitable size for any num- 
ber of cogs you choose to have to work into one another, 
take the following 



RULE. 

Draw lines to represent your shafts, in their proper 
direction, with respect to each other, to intersect A; then 
take from any scale of equal parts, as feet, inches, or 
quarters, as many parts as your wheels are to have cogs, 
and at that distance from the, respective shafts, draw the 
dotted lines a, b, c, d, for 21 and 20 cogs ; and from where 
they cross at e, draw e, A. On this line, which makes 
the right bevel, the pitch circles of the wheels will meet, 
to contain that proportion of cogs of any pitch. 

Then, to determine the size of the wheels to suit any 
particular pitch, take from the table of pitch circles, the 
radius in measures of the pitch, and apply it to the centre 
of the shaft, and the bevel line A e, taking the distance 
at right angles with the shaft; and it will show the point 
in which the pitch circles will meet, to suit that particu- 
lar pitch. 

By the same rule, the sizes of the wheels at B and C 
are found. 

Wheels of this kind, when made of cast iron, answer 
exceedingly well. 

The advantages of this kind of gear arc, 

1. They have very little friction, or sliding of parts. 

2. We can make the cogs of any width of bearing we 
choose; therefore they will wear a great while. 

3. By them we can set the shafts in any direction de- 
sired, to produce the necessary movements. 

Their disadvantage is 

They require to be kept exactly of the right depth in 
gear, so that the pitch circles meet constantly, else they 
will not run smooth, as is the case with spur gears. 

The universal joint, as represented, fig. 43, may be 



CHAP. VI.] OF MATCHING WHEELS, &C. 201 

applied to communicate motion, instead of bevel gear, 
where the motion is to be the same, and the angle not 
more than 30 or 40 degrees. This joint may be con- 
structed by a cross, as in the figure, or by four pins, fas- 
tened at right angles on the circumference of a hoop or 
solid ball. It may sometimes serve to communicate the 
motion, instead of two or three face wheels. The pivots, 
at the end of the cross, play in the ends of the semicir- 
cles. It is best to screw the semicircles to the blades, 
that they may be taken apart. 



article 82. 



OF MATCHING WHEELS TO MAKE THE COGS WEAR EVEN. 

Great care should be taken, in matching or coupling 
the wheels of a mill, that their number of cogs be not 
such that the same coo-s will often meet: because, if two 
soft ones meet often, they will both wear away faster than 
the rest, and destroy the regularity of the pitch, whereas, 
if they are continually changing, they will wear regular, 
even if they be at first a little irregular. 

For finding how often wheels will revolve before the 
same cogs meet again, take the following 



RULE. 

1. Divide the cogs in the greater wheel by the cogs 
in the lesser; and if there be no remainder, the same cogs 
will meet once every revolution of the great wheel. 

2. If there be a remainder, divide the cogs in the lesser 
wheel by the said remainder, and if it divide them equally 
the quotient shows how often the great wheel will revolve 
before the same cogs meet. 

3. But if it will not divide equally, then the great 
wheel will revolve as often as there are cogs in the small 
wheel, and the small wheel as often as there are cogs in 
the large wheel, before the same cogs meet : they 



202 OF ROLLING SCREENS AND FANS. [CHAP. VI. 

never can be made to change more frequently than 
this. 



EXAMPLE. 

Given, wheels of 13 and 17 cogs; required, how often 
each will revolve before the same cogs meet again. 
Then 13)17(1 
13 

4)13(3 

12 , Answer. 

— Great wheel 13, and 
1 Small wheel 17 revolutions. 



article 83. 

THEORy OF ROLLING SCREENS AND FANS, FOR SCREENING AND FAN- 
NING THE WHEAT IN MILLS. 

Let fig. 42, Plate V. represent a rolling screen and 
fan, fixed for cleaning wheat in a merchant mill. DA 
the screen, AF the fan, AB the wind tube, 3 feet deep 
from a to b, and 4 inches wide, in order that the grain 
may have a good distance to fall through the wind, to 
give time and opportunity for the light parts "to be car- 
ried forward, away from the heavy parts. Suppose the 
tube to be of equal depth and width for the whole of its 
length, except where it communicates with the tight 
boxes or garners under it; namely: C for the clean wheat, 
S for the screenings and light wheat, and c for the cheat, 
chaff, &c. Now, it is evident, that if wind be driven into 
the tube at A, and if it can no where escape, it will pass 
on to B, with the same force as at A, let the tube be of 
u.nj length or direction; and any thing which it will move 
at A, it will carry out at B, if the tube be of an equal size 
all the way. 

It is also evident that if we shut the holes of the fan 
at A and F, and let no wind into it, none can be forced 
into the tube ; hence, the best way to regulate the blast 



CHAP. VI.] OF ROLLING SCREENS AND FANS. 203 

is, to fix shutters sliding at the air holes, to give more or 
less feed, or air, to the fan, so as to produce a blast suf- 
ficient to clean the grain. 

The grain enters, in a small stream, into the screen at 
D, where it passes into the inner cylinder. The screen 
consists of two cylinders of sieve wire; the inmost one 
has the meshes so open as to pass all the wheat through 
it to the outer one, retaining only the white caps, large 
garlic, and every thing larger than the grain of the wheat, 
which falls out at the tail A. 

The outer cylinder is so close in the meshes, as to re- 
tain all good wheat, but to sift out the cheat, cockle, 
small wheat, garlic, and every thing less than good 
grains of wheat; the wheat is delivered out at the tail of 
the outer cylinder, which is not quite as long as the in- 
ner one, whence it drops into the wind tube at a ; and as 
it falls from a to b, the wind carries off every thing lighter 
than good wheat ; namely: cheat, chaff, light garlic, dust, 
and light rotten grains of wheat; but, in order to effect 
this completely, it should fall, at least, 3 feet through the 
current of wind. 

The clean wheat falls into the funnel b, and thence 
into the garner C, over the stones. The light wheat, 
screenings, &c. fall into garner S, and the chaff settles 
into the chaff room c. The current slackens in passing 
over this room, and drops the chaff, but resumes its full 
force as soon as it is over, and carries out the dust 
through the wall at B. To prevent the current from 
slackening too much, as it passes over S and c, and un- 
der the screen, make the passages, where the grain comes 
in and goes out, as small as possible, not more than half 
an inch wide, and as long as necessary. If the wind 
escapes any where but at B, it defeats the object, and 
carries the dust into the mill. Valves may be fixed 
to shut the passages by a weight or spring, so that the 
weight of the wheat, falling on them, will open them 
just enough to let it pass, without suffering any wind to 
escape. 

The fan is to be so set as to blow both the wheat and 
screenings, and carry out the dust. It is to be recol- 



204 OF GUDGEONS. [CHAP. VII. 

lected, also, that the wind cannot escape into the garners 
or screen-room, if they are tight ; for as soon as they are 
full no more can enter. 

By careful attention to the foregoing principle, we may 
fix fans to answer our purposes. 

The principal things to be observed in fixing screens 
and fans, are, 

1. Give the screen 1 inch to the foot fall, and between 
15 and 18 revolutions in a minute. 

2. Make the fan blow strong enough, let the wings be 
3 feet wide, 20 inches long, and revolve. 140 times in a 
minute. 

3. Regulate the blast by giving more or less feed of 
wind. 

4. Leave no place for the wind to escape but at the 
end through the wall. 

5. Wherever you want it to blow hardest, there make 
the tube narrowest. 

6. Where you want the chaff and cheat to fall, there 
widen the tube sufficiently. 

7. Make the fans blow both the wheat and screenings, 
and carry the dust clear out of the mill. 

8. The wind tube may be of any length, and either 
crooked or straight, as may best suit ; but no where small- 
er than where the wheat falls. 



CHAPTER VII. 

ARTICLE 84. 

OF GUDGEONS, THE CAUSE OF THETR HEATING AND GETTING LOOSE, 
AND REMEDIES THEREFOR. 

The cause of gudgeons heating, is the excessive fric- 
tion of their rubbing parts, which generates the heat in 
proportion to the weight that presses the rubbing surfaces 
together, and the velocity with which they move. 



CHAP. VII.] OF GUDGEONS. 205 

The cause of their getting loose is, their heating, and 
burning the wood, or drying it, so that it shrinks in the 
bands, and gives the gudgeons room to work. 

To avoid these effects, 

1. Increase the surface of contact, or rubbing parts, 
and, if possible, decrease their velocity; so much heat will 
not then be generated. 

~~~2. Conduct the heat away from the gudgeon as fast as 
it is generated. 

To increase the surface of contact, without increasing 
the velocity, lengthen the neck or bearing part of the 
gudgeon. If the length be doubled, the weight will be 
sustained by a double surface, and the velocity remain 
the same; there will not then be so much heat generated: 
and, even supposing the same quantity of heat generated, 
there will be a double surface exposed to air, to convey 
it away, and a double quantity of matter, in which it will 
be diffused. 

To convey the heat away as fast as generated, cause 
a small quantity of water to drop slowly on the gudgeon. 

A small is better than a large quantity; it should be 
just sufficient to keep up the evaporation, and not destroy 
the polish made by the grease, which it will do, if the 
quantity be too great; and this will let the box and gud- 
geon come into contact, which will cause both to wear 
rapidly away. 

The large gudgeons, for heavy wheels, are usually 
made of cast iron. Fig. 6, Plate XL, is a perspective 
view of one of the best form; a a a a are four wings, at 
right angles with each other, extending from side to side 
of the shaft. These wings are larger, every way, at the 
end that is farthest in the shaft, than at the outer end, 
for convenience in casting them, and also, that the bands 
may drive on tight, one over each end of the wings. 
Fig. 4 is an end view of the shaft, with the gudgeon in 
it and a band on the end; these bands, being put on hot, 
become very tight as they cool, and, if the shaft be dry, 
will not get loose, but will do so if green; but, by driving 
a few wedges along side of each wing, it can be easily 



206 OF GUDGEONS. [CHAP. VII. 

fastened, by any ordinary band, without danger of 
moving it from the centre. 

One great use of these wings is, to convey away the 
heat from the gudgeon to the bands, which are in con- 
tact with the air ; by thus distributing it through so much 
metal, with so large a surface exposed to the air, the heat 
is carried off as fast as generated, and therefore can 
never accumulate to a degree sufficient to burn loose, as 
it is apt to do in common gudgeons of wrought iron. 

These gudgeons should be made of the best hard me- 
tal, well refined, in order that they may wear well, and 
not be subject to break; but of this there is but little 
danger, if the metal be good. I propose, sometimes, to 
have wings cast separate from the neck, as represented 
in fig. 4, Plate XL ; where the inside light square shows 
a mortise for the steeled gudgeon, fig. 8, to be fitted into, 
with an iron key behind the wings, to draw the gudgeon 
tight, if ever it should work loose : when thus made, it 
may be taken out, at any time, to repair. 

This plan would do well for step-gudgeons for heavy 
upright shafts, such as those of tub-mills. 

When the neck is cast with the wings, the square part 
in 'the shaft need not be larger than the light square, re- 
presenting the mortise.* 

* Grease of any kind, used with a drill, in boring cast iron, prevents it from 
cutting, but will, on the contrary, make it cut wrought iron, or steel much faster. 
This quality in cast iron renders it most suitable for gudgeons, and may be the 
principal cause why cast iron gudgeons have proved much better than any one ex- 
pected. Several of the most experienced and skilful mill-wrights and millers as- 
sert that they have found cast gudgeons to run on cast boxes better than on stone 
or brass. In one instance they have carried heavy overshot wheels, which turned 
seven feet mill-stones, they have run for ten years, doing much work; and have 
hardly worn off the sand marks. 



CHAP. VIII.] OF MILL-DAMS. 207 



CHAPTER VIII. 

ARTICLE 85. 

ON BUILDING MILL-DAMS, LAYING FOUNDATIONS, AND BUILDING 
MILL-WALLS. 

There are several points to be attained, and dangers 
to be guarded against, in building mill-dams. 

1. Construct them so, that the water, in tumbling over 
them, cannot undermine their foundations at the lower 
side.* 

2. And so that heavy logs, or large pieces of ice, float- 
ing down cannot catch against any part of them, but will 
slide easily over.t 

* If you have not a foundation of solid rocks, or of stone, so heavy that the 
water will never move them, there should be such a foundation made with great 
stones, not lighter than mill-stones, (if the stream he heavy and the fall great,) 
well laid, as low and as close as possible, with their up-stream end lowest, to pre- 
vent any thing from catching under them. But if the bottom be sand or clay, 
make a foundation of the trunks of long trees, laid close together on the bottom 
of the creek, with their butt-ends down stream, as low and as close as possible, 
across the whole tumbling space. On these the dam may be built, either of stone 
or wood, leaving 12 or 15 feet below the breast or fall, for the water to fall upon. 
See fig. 3, Plate X., which is a front view of a log dam, showing the position of 
the logs; also, of the stones in the abutments. 

f If the dam be built of timber and small stones, &c, make the breast perpen- 
dicular, with straight logs, laid close one upon another, putting the largest, longest, 
and best logs on the top; make another wall of logs 12 or 1 5 'feet up-stream, laying 
them close together, to prevent lamprey eels from working through them; they 
are not to be so high as the other, by 3 feet; tie these walls together, at every 6 
feet, with cross logs, with the butts down-stream, dove-tailed and bolted strongly 
to the logs of the lower wall, especially the upper log, which should be strongly 
bolted down to them. The spaces between these log walls, are to be filled up 
with stones, gravel, &c. Choose a dry season for this work; then the water will 
run through the lower part while you build the upper part tight. 

To prevent any thing from catching against the top log, flag the top of the dam 
with broad or long stones, laying the down-stream end on the up-stream side of 
the log, to extend a little above it, the other end lowest, so that the next tier of 
stones will lap a little over the first; still getting lower, as you advance up-stream. 
This will glance logs, &c. over the dam, without their catching against any thing. 
If suitable stones cannot be had, I would recommend strong plank or small logs, 
laid close together, with both ends pinned to the top logs of the wall, the up- 
stream end being 3 feet lower than the other. But if plank is to be used, there need 
only be a strong frame raised on the foundation logs, to support the plank or the 
timber it is pinned to. See a side view of this frame, fig. 45, Plate IV. Some 
plank the breast to the front posts, and fill the hollow space with stones 



208 OP BUILDING MILL-DAMS. [CHAP. VIII. 

3. Build them so that the pressure of force of the cur- 
rent of the water will press their parts more firmly to- 
gether.* 

4. Give them a sufficient tumbling space to vent all the 
water in time of freshets.t 

5. Make the abutments so high, that the water will not 
overflow them in time of freshets. 

6. Let the dam and mill be a sufficient distance apart, 
so that the dam will not raise the water on the mill, in 
time of high flood.f 



and gravel; but this may be omitted, if the foundation logs are sufficiently long 
up-stream, under the dam, to prevent the whole from floating away. First, stone, 
and then gravel, sand, and clay, are to be filled in above this frame, so as to stop 
the water. If the abutments be well secured, the dam will stand well. 

A plank laid in a current of water, with the up-stream end lowest, set at an an- 
gle of 22§ degrees, with the horizon or current of the water, will be held firmly to 
its place by the force of the current, and, in this position, it requires the greatest 
force to remove it; and the stronger the current, the firmer it is held to its place; 
— this points out the best position for the breast of dams. 

* If the dam be built of stone, make it in the form of an arch or semicircle, stand- 
ing up-stream, and endeavour to fix strong abutments on each side, to support the 
arch; then, in laying the stones, put the widest end up-stream, and the more they 
are forced down-stream, the tighter they will press together. All the stones of 
a dam should be laid with their up-stream ends lowest, and the other end lapped 
over the preceding, like the shingles or tiles of a house, to glance every thing 
smoothly over, as at the side 3, of fig. 3, Plate X. The breast may be built up with 
stone, either on a good rock or log foundation, putting the best in front, leaning a 
little up-stream, and on the top lay one good log, and another 15 feet up-stream 
on the bottom, to tie the top log to, by several logs, with good butts, down-stream, 
dove-tailed and bolted strongly, both at bottom and top of the top and up-stream 
logs ; fill in between them with stone and gravel, laying large stones slanting next 
the top log, to glance any thing over it. This will be much better than to build 
all of stone; because if one at top gives way, the breach will increase rapidly, 
and the whole go down to the bottom. 

t If the tumbling space be not long enough, the water will be apt to overflow 
the abutments ; and if they be of earth or loose stones, they will be broken down, 
and perhaps, a very great breach made. If the dam be of logs, the abutments 
will be best made of stone, laid as at the side 3, in fig. 3; but if stone is not to be 
had, they must be made of wood, although it will be subject to rot soon, being 
above water. 

J I have, in many instances, seen a mill set so close to the dam, that the pier- 
head, or forebay, was in the breast, so that, in case of a leak or breach about the 
forebay, or mill, there is no chance of shutting off the water, or conveying it 
another way; but all must be left to its fate. Such mills are frequently broken 
down, and carried away; even the mill-stones are sometimes carried a consider- 
able distance down the stream, buried under the sand, and never found. 

The great danger from this error will appear more plainly, if we suppose six 
mills on one stream, one above the other, each at the breast of the dam, and a 
great flood to break the first or uppermost dam, say through the pier head, carry- 
ing with it the mill, stones and all: this so increases the flood, that it overflows 
the next dam, which throws the water against the mill, and it is taken away ; the 
water of these two dams has now so augmented the flood, that it carries every 
mill before it until it comes to the dam of the sixth, which it sweeps away also; 
but suppose this dam to be a quarter of a mile above the mill, which is set well 



CHAP. VIII.] ON BUILDING MILL-WALLS. 209 



ARTICLE 86. 



ON BUILDING MILL-WALLS. 

The principal things to be considered in building mill- 
walls, are, 

1. To lay the foundations with large, good stones, so 
deep as to be out of danger of being undermined, in case 
of such an accident as the water breaking through at the 
mill.* 

2. Set the centre of gravity, or weight of the wall, on 
the centre of its foundation.! 

into the bank, the extra water that is thrown into the canal, runs over at the waste 
left in its banks for the purpose; and the water having a free passage by the mill, 
does not injure it, whereas, had it been at the breast of the dam, it must have 
gone away with the rest. A ease, similar to this, actually happened in Virginia, 
in 1794; all the mills and dams on Falling Creek, in Chesterfield county, were 
carried away at once, except the lowest, (Mr. Wardrope's,) whose dam, having 
broke, the year before, was rebuilt a quarter of a mile higher up; by which means 
his mill was saved. 

* If the foundation be not good, but abounding with quick-sands, the wall cannot 
be expected to stand, unless it be made good by driving piles until they meet the 
solid ground; on the top of these may be laid large, flat pieces of timber, for the 
walls to be built on; they will not rot under water, when constantly excluded 
from the air. 

f It is a common practice to build walls plumb outside, and to batter them from 
the inside; which throws their centre of gravity to one side of their base. If, 
therefore, it settles any, it will incline to fall outwards. Mill-walls should be 
battered so much outside, as to be equal to the offset inside, to cause the whole 
weight to stand on the centre of the foundation, unless it stands against a bank, 
as the wall next the wagon, in Plate VIII. The bank is very apt to press the 
wall inwards, unless it stands battering. In this case, build the side against the 
bank plumb, even with the ground, and then begin to batter it inwards. The 
plumb rules should be made a little widest at the upper end, so as to give the 
wall the right inclination, according to its height; to do which, take a line, the 
length equal to the height of the wall, set one end, by a compass point, in the 
lower end of the plumb-rule, and strike the plumb line ; then move the other end 
just as much as the wall is to be battered in the whole height, and it will show 
the inclination of the side of the rule, that will batter the wall exactly right. 
The error of building walls plumb outside, is frequently committed in building 
the abutments of bridges ; the consequence is, they fall down in a short time ; 
because the earth between the walls is expanded a little by very hard frost, which. 
forces the walls over. 

14 



210 ON BUILDING MILL- WALLS. [CHAP. VIII. 

3. Use good mortar, and it will, in time, become as 
hard as stone.* 

4. Arch over all the windows, doors, &c. 

5. Tie them well together by the timbers of the floors. 

* Good mortar, made of pure, well burnt limestone, properly made up with 
sharp clean sand, free from any sort of earth, loam or mud, will, in time, actually 
petrify, and turn to the consistence of a stone. It is better to put too much sand 
into your mortar than too little. Workmen choose their mortar rich, because it 
works pleasantly; but rich mortar will not stand the weather so well, nor grow 
so hard as poor mortar. If it were all lime, it would have little more strength 
than clay. 



CHAP. IX.] DESCRIPTION, &C. 211 



PART THE THIRD. 



CHAPTER IX. 



DESCRIPTION OF THE AUTHOR S IMPROVEMENTS IN THE MACHINERY 
FOR MANUFACTURING GRAIN INTO MEAL AND FLOUR. 

ARTICLE 87. 

INTRODUCTORY REMARKS. 

These improvements consist of the invention and ap- 
plication of the following machines ; namely :— 

1. The Elevator. 

2. The Conveyer. 

3. The Hopper-boy. 

4. The Drill. 

5. The Descender. 

These five machines are variously applied, in different 
mills, according to their construction, so as to perform 
every necessary movement of the grain, and meal, from 
one part of the mill to another, or from one machine to 
another, through all the various operations from the time 
the grain is emptied from the wagoner's bag, or from the 
measure on board the ship, until it be completely manu- 
factured into flour, either superfine or of other qualities, 
and separated, ready for packing into barrels, for sale or 
exportation. All which is performed by the force of the 
water, without the aid of manual labour, excepting to set 
the different machines in motion, &c. This lessens the 
labour and expense of attendance of flour mills, fully one- 
half. The whole, as applied, is represented in Plate 
VIII. 



212 THE ELEVATOR AND CONVEYER. [CHAP. IX. 



ARTICLE 



1. OF THE ELEVATOR. 



The elevator is an endless strap, revolving over two 
pulleys; one of which is situated at the place whence 
the grain or meal is to be hoisted, and the other where 
it is to be delivered; to this strap is fastened a number 
of small buckets, which fill themselves as they pass under 
the lower pulley, and empty themselves as they pass 
over the upper one. To prevent any waste of what may 
spill out of these buckets, the strap, buckets, and pul- 
leys, are all enclosed, and work in tight cases, so that 
what spills will descend to the place from whence it was 
hoisted. AB, in fig. 1, Plate VI., is an elevator for 
raising grain, which is let in at A, and discharged at B, 
into the spouts leading to the different garners. Fig. 2, 
is a perspective view of the strap, with different kinds of 
buckets, and the various modes of fastening them to the 
strap. 

2. OF THE CONVEYER. 

The conveyer KI, Plate VI., fig. 1, is an endless screw 
of two continued spirals, put in motion in a trough ; the 
grain is let in at one end, and the screw drives it to the 
other, or collects it to the centre, as at y, to run into the 
elevator (see Plate VIII., 37—36—4, and 44—45) or it 
is let in at the middle, and convej^ed each way, as 15, 16, 
Plate VIII. 

Fig. 3, Plate VI., is a top view of the lower pulley of 
a meal elevator in its case, and a meal conveyer in its 
trough, for conveying meal from the stones, into the ele- 
vator, as fast as ground. This conveyer is an eight-sided 
shaft, set on all sides with small inclining boards, called 
flights, for conveying the meal from one end of the trough 
to the other; these flights are set in spirally, as shown by 
the dotted line; but the flights being set across the spiral 
line, the principle of the machine is changed from a 



CHAP. IX.] THE HOPPER BOY. 213 

screw to that of a number of ploughs; which is found to 
answer better for conveying warm meal. 

Besides these conveying nights, there are others some- 
times necessary, which are called lifters; and set with 
their broadsides foremost, to raise the meal from one side 
of the shaft, and let it fall on the other side to cool j these 
are only used where the meal is hot, and the conveyer 
short; there may be half as many of these as of the con- 
veying flights. See 21 — 22, in Plate VIII., which is a 
conveyer, carrying the meal from three pair of stones to 
the elevator, 23 — 24. 

3. OF THE HOPPER-BOY. 

Fig. 12, Plate VII., is a hopper-boy; which consists 
of a perpendicular shaft, A B having a slow motion, (not 
above 4 revolutions in a minute,) carrying round with 
it the horizontal piece CD, which is called the arm; this, 
on the under side, is set full of small inclining boards, 
called flights, so as to gather the meal towards the cen- 
tre, or to spread it from the centre to that part of the 
arm which passes over the bolting hopper; at this part, 
one board is set broadside foremost, as E, (called the 
sweeper,) which drives the meal before it, and drops it 
into the hoppers HH, as the arms pass over them. The 
meal is generally let fall from the elevator, at the extre- 
mity of the arm, at D, where there is a sweeper, which 
drives the meal before it, trailing it in a circle the whole 
way round, so as to discharge nearly the whole of its 
load, by the time it returns to be loaded again : the 
flights then gather it towards the centre, from every part 
of the circle ; which would not be the case, if the sweep- 
ers did not lay it round; but the meal would, in this case, 
be gathered from one side only of the circle. These 
sweepers are screwed on the back of the arm, so that 
they may be raised or lowered, in order to make them 
discharge sooner or later, as may be found necessary. 

The extreme flight at each end of the arms is put on 
with a screw, passing through its centre, so that they may 
be turned to drive the meal outwards; the use of which 
is, to spread the warm meal as it falls from the elevator, 



214 THE DRILL. [CHAP. IX. 

in a ring, round the hopper-boy, while it, at the same 
time gathers, the cooled meal into the bolting hopper; 
so that the cold meal may be bolted, and the warm meal 
spread to cool, by the same machine, at the same time, 
if the miller chooses so to do. The foremost edge of the 
arm is sloped up in order to make it rise over the meal, 
and its weight is nearly balanced by the weight w, hung 
to one end of a cord, passing over the pulley P, and to 
the stay iron F. About 4| feet of the lower end of the 
upright shaft is made round, passing loosely through a 
round hole in the flight arm, giving it liberty to rise and 
.fall freely, to suit any quantity of meal under it. The 
flight arm is led round by the leading arm L M, there 
being a cord passed through the holes L M, at each end, 
and made fast to the flight arm D C. This cord is length- 
ened or shortened by a hitch stick N, with two holes for 
the cord to pass through, its end being passed through a 
hole at D, and fastened to the end of a stick; this cord 
must reeve freely through the holes at the end of the 
arms, in order that the ends may both be led equally. 
The flight arm falls behind the leader about l-6th part 
of the circle. The stay-iron C F E, is formed into a ring 
atv-F, which fits the shaft loosely, keeps the arm steady, 
and serves for hanging the hands of an equal height, by 
means of the screws C E. 

Fig. 13, Plate VII., is a perspective view of the under 
side of the flight arms. The arm a c, with flights and 
sweepers complete; s s s show the screws which fasten 
the sweepers to the arms. The arm c b, is to show the 
rule for laying out for the flights. When the sweeper 
at b is turned in the position of the dotted line ; it drives 
the meal outwards. Fig. 14, Plate VII., represents a 
plate of metal on the bottom of the shaft, to keep the arm 
from the floor, and 15 is the step gudgeon. 

4. OF THE DRILL. 

The drill is an endless strap revolving over two pul- 
leys, like an elevator, but set nearly horizontal, and, in- 
stead of buckets, they are small rakes fixed to the strap, 
which draw the grain or meal along the bottom of the 



CHAP. IX.] THE DESCENDER. 215 

case. See GH, plate VI., fig. 1. The grain is let in 
at H, and discharged at G. This can sometimes be ap- 
plied at less expense than a conveyer; it should be set a 
little descending ; it will move grain or meal with ease, 
and will answer well, even when a little ascending. 



5. OF THE DESCENDER. 

The descender is a broad, endless strap of very thin 
pliant leather, canvass, flannel, &c, revolving over two 
pulleys, which turn on small pivots, in a case or trough, 
to prevent waste, one end of which is to be lower than 
the other. See E F, Plate VI. fig. 1. The grain or 
meal falls from the elevator on the upper strap at E ; and 
by its own gravity and fall, sets the machine in motion, 
which discharges the load over the lower pulley F. 
There are two small buckets to bring up what may spill 
or fall off the strap, and lodge in the bottom of the case. 

This machine moves on the principles of an over-shot 
water wheel, and will convey meal to a considerable dis- 
tance, with a small descent. Where a motion can be 
readily obtained from the water, it is to be preferred, as 
when working by itself, it is easily stopped, and is apt 
to be troublesome. 

The crane spout is hung on a shaft to turn on pivots 
or a pin, so that it may turn every way, like a crane ; into 
this spout the grain falls from the elevator, and it can be 
directed by it into any garner. The spout is made to 
fit close, and play under a broad board, and the grain is 
let into it through the middle of this board, near the pin ; 
it will then always enter the spout. It is seen under B, 
Plate VI., fig. 1. L is a view of the under side of it, 
and M is a top view of it. The pin or shaft may reach 
down so low, that a man may stand on the floor and turn 
it by the handle x. 



216 APPLICATION OF THE MACHINES. [CHAP. X. 

CHAPTER X. 

ARTICLE 89. 

APPLICATION OF THE FOREGOING MACHINES IN THE PROCESS OF MA- 
NUFACTURING WHEAT INTO SUPERFINE FLOUR. 

Plate VIII. is not meant to show the plan of a mill, 
but merely the application and use of the foregoing ma- 
chines. 

The grain is emptied from the wagon into the spout I, 
which is set in the wall, and conveys it into the scale 
2, that is made to hold 10,' 20, 30, or 60 bushels, at 
pleasure. 

There should, for the convenience of counting, be 
weights of 60 lbs. each divided into 30, 15, 7| lbs.; 
then each large weight would show a bushel of wheat, 
and the smaller ones, halves, pecks, &c, which any one 
could count with ease. 

When the wheat is weighed, draw the gate at the 
bottom of the scale, and let it run into the garner 3; at 
the bottom of which there is a gate to let it into the ele- 
vator 4 — 5, which raises it to 5; the crane spout is to 
be turned over the great store garner 6, which commu- 
nicates from floor to floor, to garner 7, over the stones 8, 
which may be intended for shelling or rubbing the wheat, 
before it is ground, to take off all dust that sticks to the 
grain, or to break smut, fly-eaten grain, lumps of dust, 
&c. As it is rubbed, it runs into 3 again ; in its passage 
it goes through a current of wind, blowing into the tight 
room 9, having only the spout a, through the lower floor, 
for the wind to escape ; all the chaff will settle in the 
room, but most of the dust will pass out with the wind at 
a. The wheat again runs into the elevator at 4, and the 
crane spout, at 5, is turned over the screen hoppers 10 
or 11, and the grain lodged there, out of which it runs 
into the rolling screen 12, and descends through the cur- 
rent of wind made by the fan 13; the clean heavy grain 
descends, by 14, into the conveyer 15 — 16, which con- 



CHAP. X.] APPLICATION OF THE MACHINES. 217 

veys it into all the garners over the stones 7 — 17 — 18, 
and these regularly supply the stones 8 — 19 — 20, keep- 
ing always an equal quantity in the hoppers, which will 
cause them to feed regularly; as it is ground, the meal 
falls to the conveyer 21 — 22, which collects it to the 
meal elevator at 23, and it is raised to 24, whence it gent- 
ly runs down the spout to the hopper-boy at 25, which 
spreads and cools it sufficiently, and gathers it into the 
bolting hoppers, both of which it attends regularly; as it 
passes through the superfine cloths 26, the superfine flour 
falls into the packing chest 28, which is on the second 
floor. If the flour is to be loaded on wagons, it should 
be packed on this floor, that it may conveniently be rolled 
into them; but if the flour is to be put on board a vessel, 
it will be more convenient to pack on the lower floor, 
out of chest 29, and thence roll it into the vessel at 30. 
The shorts and bran should be kept on the second floor, 
that they may be conveyed by spouts into the vessel's 
hold, to save labour. 

The rubbings which fall from the tail of the 1st reel 
26, are guided into the head of the 2d reel 27, which is 
in the same chest, near the floor, to save both room and 
machinery. On the head of this reel is 6 or 7 feet of 
fine cloth, for tail flour; and next to it the middling 
stuff, &c. 

The tail flour which falls from the tail of the 1st reel 
26, and head of the 2d reel 27, and requires to be bolted 
over again, is guided by a spout, as shown by dotted line 
21 — 22, into the conveyer 22 — 23, to be hoisted again 
with the ground meal ; a little bran may be let in with it, 
to keep the cloth open in warm weather; — but if there 
be not a fall sufficient for the tail flour to run into the 
lower conveyer, there may be one set to convey it into 
the elevator, as 31 — 32. There is a little regulating 
board, turning on the joint x, under the tail of the first 
reels, to guide more or less with the tail flour. 

The middlings, as they fall, are conveyed into the eye 
of either pair of mill-stones by the conveyer 31 — 32, and 
ground over with the wheat ; this is the best way of grind- 
ing them, because the grain keeps them from being 



218 APPLICATION OF THE MACHINES. [CHAP. X. 

killed; there is no time lost in doing it, and they are re- 
gularly mixed with the flour. There is a sliding board 
set slanting, to guide the middlings over the conveyer, 
that the miller may take only such part, for grinding over, 
as he shall judge lit; a little regulating board stands be- 
tween the tail flour and middlings, to guide more or less 
into the stones, or elevator. 

The light grains of wheat, screenings, &c, after being 
blown by the fan 13, fall into the screenings garner, 32; 
the chaff is driven farther on, and settles in the chaff- 
room 33; the greater part of the dust will be carried out 
with the wind through the wall. For the theory of fan- 
ning wheat, see Art. 83.* 



To clean the Screenings. 

Draw the little gate 34, and let them into the elevator 
at 4, to be elevated into garner 10; then draw gate 10, 
and shut 11 and 34, and let them pass through the roll- 
ing screen 12 and fan 13; and as they fall at 14, guide 
them down a spout (shown by dotted lines) into the ele- 
vator at 4, and elevate them into the screen-hopper 11; 
then draw gate 11, shut 10, and let them take the same 
course over again, and return into the garner 10, &c. as 
often as necessary: when cleaned, guide them into the 
stones to be ground. 

The screenings of the screenings are now in garner 
32, which may be cleaned as before, and an inferior qua- 
lity of meal made out of them. 

By these means the wheat may be effectually separated 
from the seed of weeds, &c, and these saved for food for 
cattle. 

This completes the whole process from the wagon to 
the wagon again, without manual labour, except in pack- 
ing the flour and rolling it in. 

* The bolting reels may all be set in a line connected by jointed gudgeons, sup- 
ported by bearers. The meal, as it leaves the tail of one reel, may be introduced 
into the head of the other, by an elevator bucket, fixed on the head of the reel 
open at the side next the centre, so that it will dip up the meal, and, as it passes 
over the centre, drop it in. This improvement was made by Mr. Johnson Elli- 
cott; and by it, in many cases, many wheels and shafts, and much room may be 
saved. 



CHAP. X.] APPLICATION OF THE MACHINES. 219 



ARTICLE 90. 
OF ELEVATING GRAIN FROM SHIPS. 

If the grain come to the mill by ships, No. 35, and 
require to be measured at the mill, then a conveyer, 35 
— 4, may be set in motion by the great cog-wheel, and 
may be under or above the lower floor, as may best suit 
the height of the floor above high water. This conveyer 
must have a joint, as 36, in the middle, to give the end 
that lies on the side of the ship, liberty to rise and lower 
with the tide. The wheat, as measured, is poured into 
the hopper at 35, and is conveyed into the elevator at 4 ; 
which conveyer will so rub the grain as to answer the 
end of rubbing stones. And in order to blow away the 
dust, when rubbed off, before it enters the elevator, part 
of the wind made by the fan 13, may be brought down by 
a spout, 13 — 36, and when it enters the case of the con- 
veyer, it will pass each way, and blow out the dust at 37 
and 4. 

In some instances, a short elevator may be used, with 
the centre of the upper pulley, 38, fixed immovably, 
the other end resting on the deck, but so much aslant as 
to give the vessel liberty to raise and lower: the elevator 
will then slide a little on the deck. The case of the 
lower strap of this elevator must be considerably crooked, 
to prevent the points of the bucket from wearing by rub- 
bing in their descent. The wheat, as measured, is 
poured into a hopper, which lets it in at the bottom of 
the pulley. 

But if the grain is not to be measured at the mill, then 
fix the elevator 35 — 39, to take it out of the hold,- and 
elevate it through any conveniently situated door. The 
upper pulley is fixed in a gate that plays up and down 
in circular rabbets, to raise and lower to suit the tide and 
depth of the hold, and to reach the wheat. 40 is a draft 
of the gate, and manner of hanging the elevator in it. 
(See particular description thereof, in the latter part of 
Article 95.) 

This gate is hung by a stout rope, passing over a strong 



220 APPLICATION OF THE MACHINES. [CHAP. X. 

pulley or roller 41, and thence round the axis of the 
wheel 42, round the rim of which wheel there is a rope, 
which passes round the axis of the wheel 43, round the 
rim of which is a small rope, leading down over the pul- 
ley P, to the deck, and fastened to the cleet q; a man, 
by pulling this rope, can hoist the whole elevator; be- 
cause, if the diameter of the axis be 1 foot, and the wheel 
4 feet, the power is increased 16 fold. The elevator 
is hoisted up, and rested against the wall, until the ship 
comes to, and is fastened steadily in the right place; then 
it is set in the hold on the top of the wheat, and the bot- 
tom being open, the buckets fill as they pass under the 
pulley; a man holds by the cord, and lets the elevator 
settle as the wheat sinks in the hold, until the lower 
part of the case rests on the bottom of the hold, it being 
so long as to keep the buckets from touching the vessel; 
by this time it will have hoisted 1, 2, or 3000 bushels, ac- 
cording to the size of the ship and depth of the hold, at 
the rate of 3000 bushels per hour. When the grain ceases 
running in of itself, the man may shovel it up, till the load 
is discharged. 

The elevator discharges the wheat into the conveyer 
at 44, which conveys it into the screen-hoppers 10 — 11, 
or into any other, from which it may descend into the 
elevator 4 — 5, or into the rubbing stones 8. 

This conveyer may serve instead of rubbing stones, 
and the dust rubbed off thereby may be blown out through 
the wall at p, by a wind-spout from the fan 13, into the 
conveyer at 45. The holes at 44 and 10 — 11 are to be 
small, to let but little wind escape any where, excepting 
through the wall, where it will carry off the dust. 

A small quantity of wind might be let into the con- 
veyer 15 — 16, to blow away the dust rubbed off by it. 

The fan, to be sufficient for all these purposes, must 
be made to blow very strongly, and the strength of the 
blast may be regulated as directed by Art. 83. 



CHAP. X.] APPLICATION OF THE MACHINES. 221 



ARTICLE 91. 
A MILL FOR GRINDING PARCELS. 

Here each person's parcel is to be stored in a separate 
garner, and kept separate through the whole process of 
manufacture, which occasions much labour; almost all of 
which is performed by the machines. See Plate VI., 
fig. 1 ; which is a view of one side of the mill, containing 
a number of garners holding parcels, and a side view of 
the wheat elevator. 

The grain is emptied into the garner g, from the wa- 
gon, as shown in Plate VIII., and, by drawing the gate A, 
it is let into the elevator A B, and elevated into the crane- 
spout B, which, being turned into the mouth of the gar- 
ner-spout B C, which leads over the top of a number of 
garners, and has, in its bottom, a little gate over each 
garner; these gates and garners are all numbered with 
the same numbers, respectively. 

Suppose we wish to deposite the grain in the garner 
No. 2, draw the gate 3 out of the bottom, and shut it in 
the spout, to stop the wheat from passing along it, pass 
the hole, so that it must all fall into the garner; and 
thus proceed for the other garners 3 4 5 6, &c. These 
garners are all made like hoppers, about four inches wide 
at the floor, and nearly the length of the gamer ; but as 
it passes through the next story, it is brought to the form 
of a spout, 4 inches square, leading down to the general 
spout K A, which leads to the elevator: in each of these 
spouts is a gate numbered with the number of its garner, 
so that when we want to grind the parcel in garner 2, we 
draw the gate 2 in the lower spout, to let the wheat run 
into the elevator at A, to be elevated into the crane-spout 
B, which is to be turned over the rolling-screen, as shown 
in Plate VIII. 

Under the upper tier of garners, there is another tier 
in the next story, set so that the spouts from the bottom 
of the upper tier pass down the partitions of the lower 
tier, and the upper spouts of the lower tier pass between 
the partitions of the upper tier, to the garner-spout. 



222 APPLICATION OF THE 3IACHINES. [CHAP. X. 

These garners, and the gates leading both into and out 
of them, are numbered as the others. 

If it be not convenient to fix the descending spouts 
B C, to convey the wheat from the elevator to the gar- 
ners, and K A to convey it from the garners to the ele- 
vator again, then the conveyers r s and I K may be used 
for said purposes. 

To keep the parcels separate, there should be a crane- 
spout to the meal elevator; or any other method may be 
adopted, by which the meal of the second parcel may be 
guided to fall on another part of the floor, until the first 
parcel is all bolted, and the chests cleared out, when the 
meal of the second parcel may be guided into the hop- 
per-boy. 

I must here observe, that in mills for grinding parcels 
the tail flour must be hoisted by a separate elevator to 
the hopper-boy, to be bolted over; and not run into the 
conveyer, as shown in Plate VIII; because then the par- 
cels could not be kept separate. 

The advantages of the machinery, applied to a mill 
for grinding parcels, are very great. 

1. Because without them there is much labour in 
moving the different parcels from place to place: all 
which is here done by the machinery. 

2. The meal as it is ground, is cooled by the machi- 
nery, and bolted in so short a time, that, when the grind- 
ing is done, the bolting is also nearly finished. There- 
fore, 

3. It saves room, because the meal need not be spread 
over the floor to cool, during 12 hours, as is usual; and 
but one parcel need be on the floor at one time. 

4. It gives greater despatch, as the miller need never 
stop either stones or bolts, in order to keep parcels se- 
parate. The screenings of each parcel may be cleaned, 
as directed in Art. 89, with very little trouble ; and the 
flour may be nearly packed before the grinding is 
finished; so that if a parcel of 60 bushels arrive at the 
mill in the evening, the owner may wait till morning, 
when he may have it all finished ; he may use the offal for 
feed for his team, and proceed with his load to market. 



CHAP. X.] APPLICATION OF THE MACHINES. 223 

ARTICLE 92. 

A GRIST-MILL FOR GRINDING VERY SMALL PARCELS. 

Fig. 16, Plate VII., is a representation of a grist-mill, 
so constructed that the grist being put into the hopper, 
it will be ground and bolted and returned into the bags 
again. 

The grain is emptied into the hopper at A, and as it 
is ground it runs into the elevator at B, and is elevated 
and let run into the bolting hopper down a broad spout 
at C, and, as bolted, it falls into the bags at d. The chest 
is made to come to a point like a funnel, and a division 
made to separate the fine and coarse, if wanted, and a 
bag put under each part; on the top of this division is 
set a regulating board on a joint, as x, by which the fine 
and coarse can be regulated at pleasure. 

If the bran require to be ground over, (as it often 
doeSj) it is made to fall into a box over the hopper, and 
by drawing the little gate b, it may be let into the hop- 
per as soon as the grain is all ground, and as it is bolted 
the second time, it is let run into the bag by shutting the 
gate b, and drawing the gate c. 

If the grain be put into the hopper F, then as it is 
ground it falls into the drill, which draws it into the ele- 
vator at B, and it ascends as before. 

To keep the different grists separate; — when the 
miller sees the first grist fall into the elevator, he shuts 
the gate B or d, and gives time for it all to get into the 
bolting reel; he then stops the knocking of the shoe by 
pulling the shoe line, which hangs over the pulleys p p, 
from the shoe to near his hand, making it fast to a peg; 
he then draws the gate B or d, and lets the second grist 
into the elevator, to fall into the shoe or bolting hopper, 
giving time for the first grist to be all in the bags, and 
the bags of the second grist to be put in their places; he 
then unhitches the line from the peg, and lets the shoe 
knock again; and begins to bolt the second grist. 

If he does not choose to let the meal run immediately 
into the bags, he may have a box made with feet, to stand 



224 APPLICATION OF THE MACHINES. [CHAP. X. 

in the place of the bags, for the meal to fall in, out of which 
it may be taken and put into the bags, as fast as it is bolt- 
ed, and mixed as desired ; and as soon as the first parcel 
is bolted, the little gates at the mouth of the bags may 
be shut, while the meal is filled out of the box, and the 
second grist may be bolting. 

The advantages of this improvement on a grist-mill 
are, 

1, It saves the labour of hoisting, spreading, and cool- 
ing the meal, and of carrying up the bran to be ground 
over, sweeping the chest, and filling up the bags. 

2. It does all with great despatch, and little waste, 
without having to stop the stones or bolting-reel, to keep 
the grist separate, and the bolting is finished almost as 
soon as the grinding; therefore, the owner will be the 
less time detained. 

The chests and spouts should be made steep, to pre- 
vent the meal from lodging in them; so that the miller, 
by striking the bottom of the chest, will shake out all 
the meal. 

The elevator and drill should be so made as to clean 
out at one revolution. The drill might have a brush or 
two, instead of rakes, which would sweep the case clean 
at a revolution; and the shoe of the bolting hopper 
should be short and steep, so that it will clean out ra- 
pidly. 

The same machinery may be used for merchant-work, 
by having a crane-spout at C; or a small gate, to turn the 
meal into the hopper-boy that tends the merchant bolt. 

A mill, thus constructed, might grind grists in the 
day-time, and merchant-work at night. 

A drill is preferable to a conveyer for grist-mills, be- 
cause it may be cleaned out much sooner and better. The 
lower pulley of the elevator is twice as large in diameter 
as the pulleys of the drill; the lower pulley of the ele- 
vator, and one pulley of the drill, are on the same shaft, 
close together; the elevator moves the drill, and the pul- 
ley of the drill being smallest, gives room for the meal 
to fall into the backets of the elevator. 



CHAP. X.] APPLICATION OF THE MACHINES. 225 



ARTICLE 93. 

OF ELEVATING GRAIN, SALT, OR ANY GRANULAR SUBSTANCE FROM 
SHIPS INTO STORE-HOUSES, BY THE STRENGTH OF A HORSE. 

Plate VII., fig. 17, represents the elevator, and the 
manner of giving it motion; the horse is hitched to the 
end of the sweep beam A, by which he turns the upright 
shaft, on the top of which is the driving cog-wheel of 96 
cogs 2§ inches pitch, to gear into the leading wheel of 20 
cogs, on the same shaft with which is another driving 
wheel of 40 cogs, to gear into another leading wheel of 
19 cogs, which is on the same shaft with the elevator 
pulley; then, if the horse make about 3 revolutions in a 
minute (which he will do if he walk in a circle of 20 feet 
diameter) the elevator pulley will make about 30 revolu- 
tions in a minute; and if the pulley be 2 feet in diame- 
ter, and a bucket be put on every foot of the strap, to 
hold a quart each, the elevator will hoist about 187 quarts 
per minute, or 320 bushels in an hour, 3840 bushels in 
12 hours; and, for every foot the elevator is high, the 
horse will have to sustain the weight of a quart of wheat? 
say 48 feet, which is the height of the highest store- 
houses, then the horse would have to move 1 § bushels of 
wheat upwards, with a velocity equal to hi i own walk; 
which, I presume, he can do with ease, and overcome the 
friction of the machinery: From this will appear the 
great advantages of this application. 

The lower end of the elevator should stand near the 
side of the ship, and the grain, salt, &c, be emptied into 
a hopper; the upper end may pass through a door or 
window, as may be most convenient : the lower case 
should be a little crooked to prevent the buckets from 
rubbing in their descent. 



15 



226 APPLICATION OF THE MACHINES. [CHAP. X. 

ARTICLE 94. 

OF AN ELEVATOR APPLIED TO ELEVATE GRAIN, &C, WROUGHT BY A 

MAN. 

In Plate VII., fig. 18, A B, are two ratchet wheels, 
with two deep grooves in each of there, for ropes to run 
in ; they are fixed close together, on the same shaft with 
the upper pulley of the elevator, so that they will turn 
easily on the shaft the backward way, whilst a click falls 
into the ratchet, and prevents them from turning for- 
wards. Fig. 19 is a side view of the wheel, ratchet, and 
click. C D are two levers, like weavers' treadles, and 
from lever C there is a light s^aff passes to the foreside of 
the groove wheel B, and is made fast by a rope half way 
round the wheel; and from said lever C there is a rope 
passing to the backside of the wheel A; and from lever 
D there is a light staff passing to the foreside of the 
groove wheel A, and a rope to the backside of the groove 
wheel, B. 

The man who is to work this machine stands on the 
treadles, and holds by the staff with his hands ; and as 
he 'treads on D it descends, and the staff pulls the wheel 
A forward, and the rope pulls the wheel B backward, 
and as he treads on C, the staff pulls forward the wheel 
B, and the rope pulls backward the wheel A: but the 
click falls into the ratchet, so that the wheels cannot 
move forward without turning the elevator pulley: it is 
thus moved one way by the treadles ; and in order to keep 
up a regular motion, a heavy flying wheel F, is added, 
which should be of cast iron, to prevent much obstruc- 
tion from the air. 

To calculate what quantity a man can raise to any 
height, let us suppose his weight to be 150 lbs.; which is 
the power to be applied; and suppose he be able to walk 
about 70 feet up stairs in a minute, by the strength of 
both his legs and arms, or, which is the same thing, to 
move his weight on the treadles 70 steps in a minute: 
then, suppose we allow, as by Art. 29 — 42, to lose l-3d 
of the power to gain velocity and overcome friction, 
(which will be a large allowance in this case, because in 



CHAP. X.] APPLICATION OP THE MACHINES. 227 

the experiment in the table, in Art. 37, when 7 lbs. were 
charged with 6 lbs. they moved with the velocity of 2 
feet in half a second,) then there will remain 100 lbs. 
raised 70 feet in a minute, equal to 200 lbs. raised 35 feet, 
to the top of the third story, per minute, equal to 200 
bushels per hour, 2400 bushels in twelve hours. 

The great advantages of this application of the eleva- 
tor, and of this mode of applying man's strength, will ap- 
pear from these considerations; namely: he uses the 
strength of both his legs and arms, to move his weight 
only from one treadle to the other, which weight does the 
work; whereas, in carrying bags on his back, he uses the 
strength of his legs only, to raise both the weight of his 
body and the burden ; add to this, that he generally takes 
a very circuitous route to the place where he is to empty 
the bag, and returns empty; whereas, the elevator taked 
the shortest direction to the place of emptying, and is al- 
ways steadily at work. 

The man must sit on a high bench, as a weaver does, 
on which he can rest part of his weight, and rest himself 
occasionally, when the machine moves lightly, and have 
a beam above, that he may push his head against, to over- 
come extraordinary resistances. This is probably the best 
means of applying man's strength to produce rotary 
motion. 

DESCRIPTION OF PLATE IX. 

The grain is emptied into the spout A, by which it. 
descends into the garner B; whence, by drawing the gate 
at C, it passes into the elevator C D, which raises it to D, 
and empties it into the crane spout E, which is so fixed 
on gudgeons that it may be turned to any of the surround- 
ing garners, into the screen hopper F, for instance, (which 
has two parts, F and G,) out of which it is let into the 
rolling screen at H, by drawing the small gate a. It passes 
through the fan I, and falls into the little sliding-hopper 
K, which may be moved, so as to guide it into either of 
the hanging garners, over the stones, L or M, and it is 
let into the stone-hoppers by the little bags b b, as fast 
as it can be ground. When ground, it falls into the con- 



228 APPLICATION OF THE MACHINES. [CHAP. X. 

veyer N N, which carries it into the elevator at O O, 
this raises and empties it into the hopper boy at P, which 
is so constructed as to carry it round in a ring, gathering 
it gradually towards the centre, till it sweeps into the 
bolting hoppers Q Q. 

The tail flour, as it falls, is guided into the elevator to 
ascend with the meal, and, that a proper quantity may 
be elevated, there is a regulating board R, set under the 
superfine cloths, on a joint x, so that it will turn towards 
the head or tail of the reel, and send more or less into the 
elevator, as may be required. 

There may be a piece of coarse cloth, or wire, put on 
the tails of the superfine reels, that will let all pass 
through except the bran which falls out at the tail, and 
a part of which is guided into the elevator with the tail 
flour, to assist the bolting in warm weather; the quantity 
is regulated by a small board r, set on a joint under the 
ends of the reels. Beans may be used to keep the cloths 
open, and still be returned into the elevator to ascend 
again. What passes through the coarse cloth or wire, 
and the remainder of the bran, are guided into the reel S, 
to be bolted. 

To Clean wheat several times. 

Suppose the grain to be in the screen hopper E ; draw 
the gate a; shut the gate e; move the sliding hopper K, 
over the spout Kcd; and let it run into the elevator to 
be raised again. Turn the crane spout over the empty 
hopper G, and the wheat will be all deposited there nearly 
as soon as it is out of the hopper F. Then draw the gate 
e, shut the gate a; and turn the crane spout over F; and 
so on, alternately, as often as necessary. When the grain 
is sufficiently cleaned, slide the hopper K over the hole 
that leads into the stones. 

The screenings fall into a garner, hopperwise ; to clean 
them, draw the gate f, and let them run into the eleva- 
tor, to be elevated into the screen hopper F. Then pro- 
ceed with them as with the wheat, till sufficiently clean. 
To clean the fannings, draw the little gate h, and let them 
into the elevator, &c, as before. 



CHAP. XI.J CONSTRUCTION OF MACHINES. 229 

Fig. II. is a perspective view of the conveyer, as it lies 
in its troughs, at work ; and shows the manner in which 
it is joined to the pulleys, at each side of the elevator. 

Fig. III. exhibits a view of the pulley of the meal ele- 
vator, as it is supported on each side, with the strap and 
buckets descending to be filled. 

Fig. IV. is a perspective view of the under side of the 
arms of the hopper-boy, with flights complete. The 
dotted line shows the track of the flights of one arm; 
those of the other following, and tracking between them. 
A A are the sweepers. These carry the meal round in 
a ring, trailing it regularly all the way, the flights draw- 
ing it to the centre, as already mentioned. B B are the 
sweepers that drive it into the bolting hoppers. 

Fig. V. is a perspective view of the bucket of the 
wheat elevator; and shows the manner in which it is fas- 
tened, by a broad piece of leather, which passes through 
and under the elevator-strap, and is nailed to the sides 
with little tacks. 



CHAPTER XI. 

OF THE CONSTRUCTION OF THE SEVERAL MACHINES. 

ARTICLE 95. 

OF THE WHEAT ELEVATOR. 

To construct a wheat elevator, first determine how 
many bushels it should hoist in an hour, and where it 
shall be set, so as, if possible, to answer all the following 
purposes: — 

1. To elevate the grain from a wagon or ship. 

2. From the different garners into which it may be 
stored. 

3. If it be a two-story mill, to hoist the wheat from 
the tail of the fan, as it is cleaned, to a garner over the 
stones. 



230 CONSTRUCTION OF MACHINES. [CHAP. XI. 

4. To hoist the screenings, to clean them several times. 

5. To hoist the wheat from a shelling-mill, if there be 
one. 

One elevator may effect all these objects in a mill 
rightly planned, and most of them can be accomplished 
in mills ready built. 

Suppose it be wished to hoist about 300 bushels in an 
hour, make the strap 4| inches wide, of good, strong, 
white harness leather, in one thickness. It must be cut 
and joined together in a straight line, with the thickest, 
and, consequently, the thinnest ends together, so that if 
they be too thin, they may be lapped over and doubled, 
until they are thick enough singly. Then, to make 
wooden buckets, take the butof a willow or water birch, 
that will split freely; cut it in bolts, 15 inches long, and 
rive and shave it into staves, 5| inches wide, and three- 
eighths of an inch thick; these will make one bucket, each. 
Set a pair of compasses to the width of the strap, and 
make the sides and middle of the bucket equal thereto at 
the mouth, but let the sides be only two-thirds of that 
width at the bottom, which will make it of the form of 
fig.. 9, Plate VI.; the ends being cut a little circular, to 
make the buckets lie more closely to the strap and wheel, 
as it passes over. Make a pattern of the form of fig. 9, 
by which to describe all the rest. This makes a bucket 
of a neat form, to hold about 75 solid inches, or somewhat 
more than a quart. To make them bend to a square at 
the corners e c, cut a mitre square across where they are 
to bend, about 2-8ths through; boil them and bend them 
hot, tacking a strip of leather across them, to hold them 
in that form until they get cold, and then put bottoms to 
them of the thin skirts of the harness leather. These 
bottoms are to extend from the lower end to the strap 
that binds it on. To fasten them on well, and with de- 
spatch, prepare a number of straps, If inch wide, of 
the best cuttings of the harness leather; wet them and 
stretch them' as hard as possible, which reduces their 
width to about If inch. Nail one of these straps to 
the side of a bucket, with 5 or 6 strong tacks that will 
reach through the buckets, and clinch inside. Then take 
a 1§ inch chisel, and strike it through the main strap 



CHAP. XI.] CONSTRUCTION OF MACHINES. 231 

about a quarter of an inch from each edge, and put one 
end of the binding-strap through the slits, draw the 
bucket very closely to the strap, and nail it on the other 
side of the bucket, which will finish it. See B in fig. 2. 
Plate VI. C is a meal-bucket fastened in the same man- 
ner, but is bottomed only with leather at the lower end, 
the main strap making the bottom side of it. This is the 
best way I have yet discovered, to make wooden buckets. 
The straps of the harness leather, out of which the ele- 
vator-straps are cut, are generally about enough to com- 
plete the buckets. 

To make Sheet-Iron Buckets. 

Cut the sheet in the form of fig. 8, Plate VI., making 
the middle part, c, and the sides, a and b, nearly equal to 
the width of the strap, and nearly 5| inches long, as be- 
fore. Bend them to a right angle at every dotted line, 
and the bucket will be formed : — c will be the bottom 
side next to the strap; and the little holes a a and b b 
will meet, and must be riveted to hold it together. The 
two holes c are for fastening it to the straps by rivets. 
The part a b is the part that dips up the wheat, and the 
point, being doubled back, strengthens it, and tends to 
make it wear well. The bucket being completely formed, 
and the rivet holes made, spread one out again, as fig. 
8, to describe all the rest by, and to mark for the holes, 
which will meet again when folded up. They are fas- 
tened to the strap by two rivets with thin heads, put in- 
side the bucket, and a double burr of sheet-iron put on 
the under side of the strap, which fastens them on very 
tightly. See A, fig. 2, Plate VI. These buckets will 
hold about 1,3- quarts or 88 cubic inches. This is the 
best way I have found to make sheet-iron buckets. D is 
a meal-bucket of sheet-iron, riveted on by two rivets, 
with their heads inside the strap; the sides of the buckets 
are turned a little out, and holes made in them, for the 
rivets to pass through. Fig. 1 1 , is the form of one spread 
out, and the dotted lines show where they are to be bent, 
at right angles to form them. The strap forms the bot- 
tom side of these buckets. 



232 CONSTRUCTION OF MACHINES. [CHAP. XL 

Make the pulleys 24 inches in diameter, as thick as 
the strap is wide, and half an inch higher in the middle 
than at the sides, to make the strap keep on ; give them 
a motion of 25 revolutions in a minute, and put on a sheet 
iron bucket for every 15 inches; then 125 buckets will 
pass per minute, which will carry 162 quarts, and hoist 
300 bushels in an hour, and 3600 bushels in 12 hours. 

If you wish to hoist faster, make the strap wider, the 
buckets larger in proportion, and increase the velocity 
of the pulley, but not to above 35 revolutions in a minute, 
nor place more buckets than one for every 12 inches, 
otherwise they will not empty well. A strap of 5 inches, 
with buckets 6 inches long, and of a width and propor- 
tion suiting the strap, (4§ inches wide,) will hold 1,8 
quarts each ; and 35 revolutions of the pulley will pass 
175 buckets, which will carry 315 quarts in a minute, 
and 590 bushels in an hour. If the strap be 4 inches 
wide, and the wooden buckets 5 inches deep, and, in pro- 
portion to the strap, they will hold ,8 of a quart: then, 
if there be one for every 15 inches, and the pulley makes 
27 revolutions in a minute, it will hoist 200 bushels in 
an hour. Where there is a good garner to empty the 
wheat into, this is the size they are commonly made, and 
is sufficient for unloading wagons. 

Plate VI., Fig. 6, represents the gudgeon of the lower 
pulley, fig, 7, the gudgeon for the shaft on which the 
upper pulley is fixed. Fix both the pulleys in their 
places, but not firmly, so that a line, stretched from one 
pulley to the other, will cross the shafts of gudgeons at 
right angles. This must always be the case'to make the 
straps work fairly. Put on the strap with the buckets; 
draw it tightly, and buckle it; put it in motion, and if it 
do not keep fairly on the pulleys, their position may be 
altered a little. Observe how much the descending strap 
swags by the weight of the buckets, and make the case 
round it so curved, that the points of their buckets will 
not rub in their descent, which will cause them to wear 
long and work easily. The side boards need not be made 
crooked in dressing out, but may be bent sufficiently by 
sawing them halfway, or two-thirds through, beginning 



CHAP. XI.] CONSTRUCTION OF MACHINES. 233 

at the upper edge, holding the saw very much aslant, 
the point downwards and inwards, so that in bending, the 
parts will slip past each other. The upper case must be 
nearly straight; for if it be made much crooked, the 
buckets will incline to turn under the strap. Make the 
cases 3-4ths of an inch wider inside, than the strap and 
buckets, and If inches deeper, that they may play free- 
ly; but do not give them room to turn upside down. If 
the strap and buckets be 4 inches, then make the side 
boards 5|, and the top and bottom boards 6| inches wide, 
of inch boards. Be careful that no shoulders nor nail- 
points be left inside of the cases, for the buckets to catch 
in. Make the ends of each case, where the buckets en- 
ter as they pass over the pulleys, a little wider than the 
rest of the case. Both the pulleys are to be nicely cased 
round to prevent waste, not leaving room for a grain to 
escape, continuing the case of the same width round the 
top of the upper, and bottom of the lower pulley; then if 
any of the buckets should ever get loose, and stand askew, 
they will be kept right by the case ; whereas, if there 
were any ends of boards or shoulders, they would catch 
against them. See A B, fig. 1, Plate VI. The bottom 
of the case of the upper pulley must be descending, so 
that what grain may fall out of the buckets in passing 
over the pulleys, may be guided into the descending 
case. The shaft passing through this pulley is made 
round where the case fits to it: half circles are cut out 
of two boards, so that they meet and embrace closely. 
The undermost board, where it meets the shaft, is ci- 
phered off inside next the pulley, to guide the grain in- 
ward. But it is full as good a way to have a strong 
gudgeon to pass through the upper pulley, with a tenon 
at one end, to enter a socket, which may be in the shaft, 
that is to give it motion. This will suit best where the 
shaft is short, and has to be moved to put the elevator 
out of, and into gear. 

The way that I have generally cased the pulleys is as 
follows, namely; the top board of the upper strap-case 
and the bottom board of the lower strap-case, are ex- 
tended past the lower pulley to rest on the floor ; and the 



234 CONSTRUCTION OF MACHINES. [CHAP. XI. 

lower ends of these boards are made two inches narrower, 
as far as the pulley-case extends; the side board of the 
pulley is nailed, or rather screwed, to them, with wooden 
screws. The rest of the case boards join to the top of 
the pulley-case, both being of one width. The block, 
which the gudgeons of this pulley run in, is screwed fast 
to the outside of the case boards ; the gudgeons do not 
pass quite through, but reach to the bottom of the hole, 
which keeps the pulley in its place. 

The top and bottom boards, and, also, the side-boards 
of the strap-cases, are extended past the upper pulley, 
and the side-boards of the pulley case are screwed to 
them; but this leaves a vacancy between the top of the 
side-boards, of the strap-cases, and shoulders for the buck- 
ets to catch against, and ftiis vacancy is to be filled up 
by a short board, guiding the buckets safely over the up- 
per pulley. The case must be as close to the points of 
the buckets, where they empty, as is safe, that as little 
as possible may fall down again. There is to be a long 
hole cut into the case at B, for the wheat to fall out at, 
and a short spout guiding it into the crane spout. The 
top of the short spout next B, should be loosely fastened 
h\ with a button, that it may be taken off, to examine if 
the buckets empty well, &c. Some neat workmen have 
a much better way of casing the pulleys, which is not 
easily described ; what I have described is the cheapest, 
and answers very well. 

The wheat should be let in at the bottom, to meet the 
buckets; and a gate should shut as near to the point of 
them as possible, as at A, fig. 1, Plate VI. Then, if 
the gate be drawn sufficiently to fill the buckets, and the 
elevator be stopped, the wheat will stop running in, and 
the elevator will be free to start again; but if it had been 
let in any distance up, then, when the elevator stopped, 
it would fill from the gate to the bottom of the pulley, 
and the elevator could not start again. If it be, in an} r 
case, let in at a greater distance up, the gate should be 
so fixed that it cannot be drawn so far as to let in the 
wheat faster than the buckets can take it, else the case 
will fill and stop the buckets. If it be let in faster at the 



CHAP. XI.] CONSTRUCTION OF MACHINES. 235 

hindmost side of the pulley than the buckets will carry 
it, the same evil will occur; because the buckets will 
push the wheat before them, being more than they can 
hold, and give room for too much to come in ; therefore, 
there should be a relief gate at the bottom, to let the 
wheat out, should too much happen to get in. 

The motion is to be given to the upper pulley of all 
elevators, if it can be done, because the weight in the 
buckets causes the strap to hang tightly on the upper, 
and slackly on the lower pulley; therefore, the upper 
pulley will carry the greatest quantity without slipping. 
All elevators should stand a little slanting, because they 
will discharge the better. The boards for the cases 
should be of unequal lengths, so that two joints may ne- 
ver come close together; this greatly strengthens the 
case. Some have joined the cases at every floor; which 
is a great error. There must be a door in the ascend- 
ing case, at the place most convenient for buckling the 
strap, &c. &c. 

Of the Crane Spout. 

To make a crane spout, fix a board 18 or 20 inches 
broad, truly horizontal, or level, as a, under B, fig. 1, 
Plate VI. Through the middle of this board the wheat 
is conveyed, by a short spout, from the elevator. Then 
make the spout of 4 boards, 12 inches wide at the upper, 
and about 4 or 5 inches at the lower end. Cut the up- 
per end off aslant, so as to fit nicely to the bottom of the 
board; hang it to a strong pin, passing through the broad 
board near the hole through which the wheat passes, so 
that the spout may be turned in any direction, and still 
cover the hole, at the same time it is receiving the wheat, 
and guiding it into any garner, at pleasure. In order 
that the pin may have a strong hold of the board and 
spout, there must be a piece of scantling, 4 inches thick, 
nailed on the top of the board, for the pin to pass through; 
and another to the bottom, for the head of the pin to rest 
on. But if the spout be long and heavy, it is best to 
hang it on a shaft, that may extend down to the floor, or 
below the collar-beams, with a pin through it, as x, to 



236 CONSTRUCTION OF MACHINES. [CHAP. XI. 

turn the spout by. In crane spouts for meal, it is some- 
times best to let the lower board reach to, and rest on 
the floor. If the elevator-cases and crane spout be well 
fixed, there can neither grain nor meal escape, or be 
wasted, that enters the elevator, until it comes out at the 
end of the crane-spout again. 

Of an Elevator to elevate Wheat from a Ship's Hold* 

Make the elevator complete (as it appears 35 — 39, 
Plate VIII.) on the ground, and raise it to its place af- 
terwards. The pulleys are to be both fixed in their 
places and cased; and the blocks that the gudgeon of the 
upper pulley is to run in, are to be riveted fast to the 
case-boards of the pulley, and these case-boards screwed 
to the strap-cases by long screws, reaching through the 
case-boards edgeways. Both sides of the pulley-case are 
fastened by one set of screws. On the outside of these 
blocks, round the centre of the gudgeons, are circular 
knobs, 6 inches diameter, and 3 inches long, strongly ri- 
veted to keep them from splitting off, because, by these 
knobs the whole weight of the elevator is to hang. In 
the moveable frame 40, o o, o o, are these blocks with 
their knobs, which are let into the pieces of the frame 
B C r s. The gudgeons of the upper pulley p pass 
through these knobs and play in them. Their use is to 
bear the weight of the elevator that hangs by them ; the 
gudgeons, by this means, bear only the weight of the 
strap and its load, as is the case with other elevators. 
Their being circular, gives the elevator liberty to swing 
out from the wall to the hold of the ship. 

The frame 40 is made as follows; the top piece AB is 
9 by 8 inches, strongly tenoned into the side pieces AD 
and BC with double tenon, which side pieces are 8 by 
6. The piece r s is put in with a tenon, 3 inches thick, 
which is dove-tailed, keyed, and draw-pinned, with 
an iron pin, so that it can be easily taken out. In each 
side piece AD and BC there is a row of cogs, set in a 
circle, that are to play in circular rabbets in the posts 

* See the description of this elevator in Art. 90. 



CHAP. XI.] CONSTRUCTION OF MACHINES. 237 

p. 41. These circles are to be described with a radius, 
whose length is from the centre of the joint gudgeons G, 
to the centre of the pulley 39 ; and the post must be set 
up, so that the centre of the circle will be the centre of 
the gudgeon G ; then the gears will be always right, al- 
though the elevator rises and falls to suit the ship or tide. 
The top of those circular rabbets ought to be so fixed, 
that the lower end of the elevator may hang near the 
wall. This may be regulated by fixing the centre of the 
gudgeon G. The length of these rabbets is regulated by 
the distance the vessel is to rise and fall, to allow the ele- 
vator to swing clear of the vessel when light, at high wa- 
ter. The best way to make the circular rabbets is, to 
dress two pieces of 2 inch plank for each rabbet, of the 
right circle, and to pin them to the posts, at such a dis- 
tance, leaving the rabbet between them. 

When the gate and elevator are completed, and tried 
together, the gate hung in its rabbets, and played up and 
down, then the elevator may be raised by the same power 
that is to raise and lower it, as described, Art. 94. 



article 96. 

OF THE MEAL ELEVATOR. 

Little need be said of the manner of constructing the 
meal elevator, after what has been said in Art. 90, ex- 
cept giving the dimensions. Make the pulleys 3| inches 
thick, and 18 inches diameter. Give them no more than 
20 revolutions in a minute. Make the strap 3| inches 
wide, of good, pliant, white harness leather; make buck- 
ets either of wood or sheet iron, to hold about half a pint 
each ; put one for every foot of the strap; make the cases 
tight, especially round the upper pulley, slanting much 
at bottom, so that the meal which falls out of the buckets 
may be guided into the descending case. Let it lean a 
little, that it may discharge the better. The spout that 
conveys the meal from the elevator to the hopper-boy, 
should not have much more than 45 degrees descent, 



238 CONSTRUCTION OP MACHINES. [CHAP. XL 

that the meal may run easily down, and not cause a dust; 
fix it so that the meal will spread thinly over its bottom 
in its descent, and it will cool the better. Cover the top 
of the spout half way down, and hang a thin, light cloth, 
at the end of this cover, to check all the dust that mav 
rise, by the fall of the meal from the buckets. Remem- 
ber to take a large cipher off the inside of the board, 
where it fits to the undermost side of the shaft of the up- 
per pulley: the meal will otherwise work out along the 
shaft. Make all tight, as directed, and it will effectually 
prevent waste. 

In letting meal into an elevator, it must be let in some 
distance above the centre of the pulley, that it may fall 
clear from the spout that conveys it in; otherwise, it will 
clog and choke. Fig. 4, Plate VI., is the double socket 
gudgeon of the lower pulley, to which the conveyer joins. 
Fig. 3, a b c d, is a top view of the case that the pulley 
runs in, which is constructed thus; a bis a strong plank, 
14 by 3 inches, stepped in the sill, dove-tailed and keyed 
in the meal-beam, and is called the main bearer. In 
this, at the determined height, are framed the gudgeon 
bearers a c b d, which are planks 15 by 1| inches, set 7| 
inches apart, the pulley running between, and resting on 
them. The end piece cd, 7 inches wide and two thick, 
is set in the direction of the strap case, and extends 5 
inches above the top of the pulley; to this the bearers 
are nailed. On the top of the bearers, above the gud- 
geons, are set two other planks, 13 by If inches rab- 
betted into the main bearer, and screwed fast to the end 
piece c d: these are 4 inches above the pulley. The bot- 
tom piece of this case slides in between the bearers, rest- 
ing on two cleets, so that it can be drawn out to empty 
the case, if it should ever, by any means, be overcharged 
with meal: this completes the case. In the gudgeon 
bearer, under the gudgeons, are mortises, made about 
12 by 2 inches, for the meal to pass from the conveyer 
in the elevator; the bottom board of the conveyer 
trough rests on the bearer of these mortises. The strap- 
case joins to the top of the pulley-case, but it is not made 
fast, but the back board of the descending case is stepped 



CHAP. XI.] CONSTRUCTION OF MACHINES. 239 

into the inside of the top of the end piece c d. The bot- 
tom of the ascending case is to be supported steadily to 
its place, and the board at the bottom must be ciphered 
off at the inside, with long and large ciphers, making 
them, at the point, only | of an inch thick ; this is to make 
the bottom of the case wide for the buckets to enter, if 
any of them should be a little askew ; the pulley-case is 
wider than the strap-cases, to give room for the meal from 
the conveyer to fall into the buckets; and, in order to 
keep the passage open, there is a piece 3 inches wide, 
and I| inches thick, put on each side of the pulley, to 
stand at right angles with each other, extending 3| inches 
at each end, past the pulley; these are ciphered off so as 
to clear the strap, and draw the meal under the buckets : 
they are called bangers. 



article 97. 



OF THE MEAL CONVEYER. 



Fig. 3, Plate VI., is a conveyer joined to the pulley of 
the elevator. (See it described, Art. 88.) Fig. 4 is the 
gudgeon that is put through the lower pulley, to which 
the conveyer is joined by a socket, as represented. Fig. 
5 is a view of the said socket and the band, as it ap- 
pears on the end of the shaft. The tenon of the gudgeon 
is square, that the socket may fit it every way alike. 
Make the shaft 5| inches diameter, of eight equal sides, 
and put on the socket and the gudgeon ; then, to lay it out 
for the nights, begin at the pulley, mark as near the end 
as possible, on the one side, and, turning the shaft 
the way it is to work, at the distance of 1| inches to- 
wards the other end, set a flight on the next side, and 
thus go on to mark for a flight on every side, still ad- 
vancing If inches to the other end, which will form the 
dotted spiral line, which would drive the meal the wrong 
way; but the flights are to be set across this spiral line, 



240 CONSTRUCTION OF MACHINES. [CHAP. XI. 

at an angle of about 30 degrees, with a line square across 
the shaft; and then they will drive the meal the right 
way, the flights operating like ploughs. 

To make the flights, take good maple, or other smooth 
hard wood; saw it into six inch lengths, split it always 
from the sap to the heart ; make pieces 2| inches wide, 
and | of an inch thick; plane. them smooth on one side, 
and make a pattern to describe them by, and make a tenon 
2| inches long, to suit a | inch auger. When they are 
perfectly dry, having the shaft bored, and the inclination 
of the flights marked by a scribe, drive them in and cut 
them off2§ inches from the shaft; dress them with their 
foremost edge sharp, taking all off from the backside, 
leaving the face smooth and straight, to push forward the 
meal; make their ends nearly circular. If the conveyer 
be short, put in lifting flights, with their broadside fore- 
most, half the number of the others, between the spires 
of them; they cool the meal by lifting and letting it fall 
over the shaft. 

To make the trough for it to run in, take 3 boards, the 
bottom one 11, back 15, and front 13 inches. Fix the 
block for the gudgeon to run in at one end, and fill the 
corners of the elects, to make the bottom nearly circular, 
that but little meal may lie in it; join it neatly to the 
pulley-case, resting the bottom on the bottom of the hole 
cut for the meal to enter, and the other end on a sup- 
porter, that it can be removed and put to its" place again 
with ease, without stopping the elevator. 

A meal elevator and conveyer thus made, of good ma- 
terials, will last 50 years, with very little repair, and save 
an immense quantity of meal from waste. The top of 
the trough must be left open, to let the stream of the 
meal out ; and a door, about 4 feet long, may be made in 
the ascending case of the elevator, to buckle the strap, 
&c. The strap of the elevator turns the conveyer, so 
that it can be easily stopped if any thing should be caught 
in it; it is dangerous to turn it by cogs. This machine 
is often applied to cool the meal, without the hopper-boy, 
and to attend the bolting-hopper, by extending it to 
a great length, and conveying the meal immediately 



CHAP. XI.] CONSTRUCTION OF MACHINES. 241 

into the hopper, which answers very well; but where 
there is room a hopper-boy is preferable. 



article 98. 



OF A GRAIN CONVEYER. 



This machine has been constructed in a variety of 
ways; the following appears to be the best, namely: 
First, make a round shaft, 9 inches diameter; and then, 
to make the spire, take strong sheet-iron, make a pattern 
3 inches broad, and of the true arch of a circle; the di- 
ameter of which (being the inside of the pattern) is to be 
12 inches; this will give it room to stretch along a 9 inch 
shaft, so as to make a rapid spiral, that will advance 
about 21 inches along the shaft every revolution. By 
this pattern cut the sheet-iron into circular pieces, and 
join the ends together by riveting and lapping them, so 
as to let the grain run freely over the joints; when they 
are joined together they will form several circles, one 
above the other, slip it on the shaft, and stretch it along 
as far as you can, till it comes tight to the shaft, and fas- 
ten it to its place by pins, set in the shaft at the back side 
of the spire, and nail it to the pins : it will now form a 
beautiful spiral, with returns 21 inches apart, which dis- 
tance is too great; there should, therefore, be two or three 
of these spirals made, and wound into each other, and all 
put on together, because, if one be put on first, the 
others cannot be got on so well afterwards; if there be 
three, they will then be 7 inches apart, and will convey 
wheat very fast. If these spirals be punched full of 
holes like a grater, and the trough be lined with sheet- 
iron, punched full of small holes, it will become an ex- 
cellent rubber; will clean the wheat of the dust down, 
that adhere to it, and supersede the necessity of any other 
rubbing machine. 

The spirals may also be formed with either wooden or 
16 



242 CONSTRUCTION OF MACHINES. [CHAP. XI. 

iron flights, set so near to each other in the spiral lines, 
as to convey the wheat from one to another. 



ARTICLE 99. 
OF THE HOPPER-BOY. 

This machine, also, has appeared under various con- 
structions, the best of which is represented by fig. 12, 
Plate VII.— (See the description Art. 88.) 

To make the flight-arms C D, take a piece of dry pop- 
lar or other soft scantling 14 feet long, 8 by 2| inches in 
the middle, 5 by If inches at the end, and straight at the 
bottom; on this strike the middle line a b, fig. 13. Con- 
sider which way it is to revolve, and cipher off the under 
side of the foremost edge from the middle line, leaving 
the edge f of an inch thick, as appears by the shaded part. 
Then, to lay out the flights, take the following 

RULE. 

Set your compasses at 4| inches distance, and, begin- 
ning with one foot in the centre c, step towards the end 
b, observing to lessen the distance one-sixteenth part of 
an inch every step; this will set the flights closer toge- 
ther at the end than at the centre. Then, to set the 
flights of one arm to track truly between those of the 
other, and to find their inclination, with one point in the 
centre c, sweep the dotted circle across every point in 
one arm; then, without altering the centre or distance, 
make the little dotted marks on the other arm, and be- 
tween them the circles are to be swept for the flights in 
it. To vary their inclination regularly, from the end 
to the centre, strike the dotted line c d half an inch from 
the centre c, and 2| inches from the middle line at d, 
and then with the compasses set to half an inch, set off 
the inclination from the dotted circles, on the line c d ; 
the line c d then approaches the middle line, the in- 



CHAP. XI.] CONSTRUCTION OF MACHINES. 243 

clination is greater near the centre than at the end, and 
varies regularly. Dove-tail the nights into the arm, ob- 
serving to put the side that is to drive the meal, to the 
line of inclination. The bottoms of them should not ex- 
tend past the middle line, the ends being all rounded and 
dressed off at the back side, to make the point sharp, 
leaving the driving side quite straight, like the flight r. 
(See them complete in the end c a.) The sweepers 
should be 5 or ,6 inches long, screwed on behind the 
flights, at the back side of the arms, one at each end of 
the arm, and one at the part that passes over the hopper: 
their use is described in Art. 88. 

The upright shaft should be 4 by 4 inches, and made 
round for about 4| feet at the lower end, to pass lightly 
through the centre of the arm. To keep the arm steady, 
there is a stay-iron 15 inches high, its legs § inch by |, 
to stride 2 feet. The ring at the top should fit the shaft 
neatly, and be smooth and rounded inside, that it may 
slide easily up and down; by this the arm hangs to the 
rope that passes over a pulley at the top of the shaft, 8 
inches diameter, with a deep groove for the rope or cord 
to run in. Make the leading arm 6 by 1| inches in the 
middle, 2 by 1 inch at the end, and 8 feet long. This 
arm must be braced to the cog-wheel above, to keep it 
from splitting the shaft by an extra stress. 

The weight of the balance w, must be so nearly equal 
to the weight of the arm, that when it is raised to the top 
it will descend quietly. 

In the bottom of the upright shaft is the step gudgeon 
(fig. 15,) which passes through the square plate 4 by 4 
inches (fig. 14;) on this plate the arm rests, before the 
flights touch the floor. The ring on the lower end of the 
shaft is less than the shaft, that it may pass through the 
arm: this gudgeon comes out, every time the shaft is 
taken out of the arm. 

If the machine is to attend but one bolting-hopper, it 
need not be above 12 or 13 feet long. Set the upright 
shaft close to the hopper, and the flights all gather as 
the end c b, fig. 13. But, if it is to attend, for the grind- 
ing of two pair of stones, and two hoppers, make it 15 
feet long, and set it between them a little to one side of 



244 CONSTRUCTION OF MACHINES. [CHAP. XL 

both, so that the two ends may not both be over the hop- 
pers at the same time, which would make it run unstea- 
dily; then the nights between the hoppers and the cen- 
tre must drive the meal outwards to the sweepers, at the 
end c a, fig. 13. 

If it be to attend two hoppers, and cannot be set be- 
tween them for want of room, then set the shaft near to 
one of them ; make the flights so that they will all gather 
to the centre, and put sweepers over the outer hopper, 
which will be first supplied, and the surplus carried to 
the other. The machine will regulate itself to attend 
both, although one should feed three times as fast as the 
other. 

If it be to attend three hoppers, set the shaft near the 
middle one, and put sweepers to fill the other two, the 
surplus will come to the centre one, and it will regulate 
to feed all three; but should the centre hopper ever stand 
while the others are going, (of either of these last appli- 
cations,) the flights next the centre must be moveable, 
that they may be turned, and set to drive the meal out 
from the centre. Hopper-boys should be driven by a 
strap in some part of their movement, that they may 
easily stop if any thing catch in them ; but many mill- 
wrights prefer cogs ; they should not revolve more than 
4 times in a minute. 



article 100. 

OF THE DRILL. 

(See the description, Art. 88.) The pulleys should 
not be less than 10 inches diameter for meal, and for 
wheat more. The case they run in is a deep, narrow 
trough, say, 16 inches deep, and 4 wide; pulleys and strap, 
3 inches. The rakes are little, square blocks of willow 
or poplar, or any soft wood, that will not split by driving 
the nails; they should all be of one size, that each may 
take an equal quantity ; they are nailed to the strap with 
long, small nails, with broad heads, which are inside the 
strap ; the meal should always be let into them above the 



CHAP. XI.] CONSTRUCTION OF MACHINES. 245 

centre of the pulley, or at the top of it, to prevent its 
choking, which it is apt to do, if let in low. The motion 
should be slow for meal, but may be more lively for 
w T heat. 

Directions for using a Hopper-boy. 

1. When the meal elevator is set in motion to elevate 
the meal, the hopper-boy must be set in motion also, to 
spread and cool it; and as soon as the circle is full, the 
bolts may be started ; the grinding and bolting may like- 
wise be carried on regularly together; which is the best 
way of working. 

2. But if you do not choose to bolt as you grind, turn 
up the feeding sweepers and let the hopper-boy spread 
and cool the meal, and rise over it; and when you begin 
to bolt, turn them down again. 

3. If you choose to keep the warm meal separate from 
the cool, shovel about 18 inches of the outside of the cir- 
cle, in towards the centre, and turn the end nights, to 
drive the meal outwards; it will then spread the warm 
meal outwards, and gather the cool meal into the bolting 
hopper. As soon as the ring is full with warm meal, 
take it out of the reach of the hopper-boy, and let it fall 
again. 

4. To mix tail flour or bran, &c, with a quantity of 
meal that is under the hopper-boy, make a hole for it in 
the meal quite to the floor, and put it in ; and the hopper- 
boy will mix it regularly with the whole. 

5. If it do not keep the hopper full, turn the feeding 
sweeper a little lower, and throw a little meal on the top 
of the arm, to make it sink deeper into the meal. If the 
spreading sweepers discharge their loads too soon, and do 
not trail the meal all round the circle, turn them a little 
lower; if they do not discharge, but keep too full, raise 
them a little. 



246 UTILITY OF THESE IMPROVEMENTS. [CHAP. XI. 

ARTICLE 101. 
OF THE UTILITY OF THESE INVENTIONS AND IMPROVEMENTS. 

In order to dry the meal in the most rapid and effectual 
manner, it is evident, that it should be spread as thinly 
as possible, and be kept in motion from the moment it 
leaves the stones, until it be cold, that it may have a fair 
opportunity of discharging its moisture, which will be 
done more effectually at that time, than after it has grown 
cold in a heap, and has retained its moisture; this imme- 
diate drying does not allow time for insects to deposite 
their eggs, which, in time, breed the worms that are often 
found in the heart of barrels of flour well packed; and, 
by the moisture being expelled more effectually, it will 
not be so apt to sour. The first great advantage, there- 
fore, is that the meal is better prepared for bolting, for pack- 
ing, and for keeping, in much less time than usual. 

2. They do the work to much greater perfection, by 
cleaning the grain and screenings more effectually, hoist- 
ing and bolting over great part of the flour, and grinding 
and bolting over the middlings, all at one operation mix- 
ing those parts that are to be mixed, and separating such 
as are to be separated. 

3. They save much meal from being wasted,.'^ they be 
well constructed, because there is no necessity for tramp- 
ling in it, which trails it wherever we walk, nor shovel- 
ling it about to raise a dust that flies away, &c. This 
article of saving will soon pay the cost of making the ma- 
chinery, and of keeping it in repair afterwards. 

4. They afford more room than they take up, because 
the whole of the meal loft that heretofore was little 
enough to cool the meal on, may be spared for other uses, 
excepting the circle described by the hopper-boy; and 
the wheat garners may be filled from *one story to ano- 
ther, up to the crane-spout, above the collar-beams, so 
that a small part of the house will hold an unusual quan- 
tity of wheat, and it may be drawn from the bottom into 
the elevator, as wanted. * 

5. They tend to despatch business, by finishing as they 



CHAP. XI.] UTILITY OF THESE IMPROVEMENTS. 247 

go; so that there is not so much time expended in grind- 
ing over middlings, which will not employ the power of 
the mill, nor in cleaning and grinding the screenings, 
they being cleaned every few days, and mixed with the 
wheat, and as the labour is easier, the miller can keep the 
stones in better order, and more regularly and steadily at 
work, especially in the night time, when they frequently 
stop for want of help; whereas, one man would be suffi- 
cient to attend six pairs of stones, running (in one house) 
with well constructed machinery. 

6. They last a long time, with but little expense of repair, 
because their motions are slow and easy. 

7. They hoist the grain and meal with less power, and 
disturb the motion of the mill much less than the old way, 
because the descending strap balances the ascending one, 
so that there is no more power used, than to hoist the 
grain or meal itself; whereas, in the old way, for every 
3 bushels of wheat, which fill a 4 bushel tub with meal, 
the tub has to be hoisted, the weight of which is equal to 
a bushel of wheat; consequently, the power used is as 3 
for the elevator to 4 for the tubs, which is one-fourth less 
with elevators than tubs; besides, the weight of 4 bushels 
of wheat, thrown at once on the wheel, always checks the 
motion; before the tub is up, the stone sinks a little, and 
the mill is put out of tune every tub full, which makes a. 
great difference in a year's grinding; this is worthy of 
notice when water is scarce. 

8. They save a great expense of attendance. One-half 
of the hands that were formerly required are now suffi- 
cient, and their labour is easier. Formerly, one hand 
was required for every 10 barrels of flour that the mill 
made daily; now, one for every 20 barrels is sufficient. 
A mill that made 40 barrels a day, required four men and 
a boy, two men are now sufficient. 



248 BILLS OP MATERIALS. [CHAP. XII. 



CHAPTER XII. 

BILLS OF MATERIALS TO BE PROVIDED FOR BUILDING AND CONSTRUCT- 
ING THE MACHINERY. 



ARTICLE 102. 

For a Wheat Elevator 43 feet high, with a Strap 4 
inches wide. 

Three sides of good, firm, white harness-leather. 

220 feet of inch pine, or other boards that are dry, of 

about 12| inches width, for the cases; these are to be 

dressed as follows: 
86 feet in length, 7 inches wide, for the top and bottom. 
86 feet in length, 5 inches wide, with the edges truly 

squared, for the side boards. 
A quantity of inch boards for the garners, as they may 

Ipe wanted. 
Sheet-iron, or a good but of willow wood, for the buckets. 
2000 tacks, 14 and 16 ounce size, the largest about half 

an inch long, for the buckets. 
3 lbs. of 8 penny, and 1 lb. of 10 penny nails, for the 

cases. 
2 dozen of large, wood screws, (but nails will do,) for 

pulley cases. 
16 feet of two inch plank, for pulleys. 
16 feet of ditto, for cog-wheels, and dry pine scantling, 

4| by 4|, or 5 by 5 inches to give it motion. 

Smith's Bill of Iron. 

1 double gudgeon | inch, (such as fig. 6, Plate VI.,) 5 
inches between the shoulders, 3| inches between the 
holes, the necks, or gudgeon part, 3 inches. 

1 small gudgeon, of the common size, f inch thick. 

1 gudgeon an inch thick, (fig. 7,) neck 3|, tang. 10 inches, 
to be next the upper pulley. 



CHAP. XII.] BILLS OP MATERIALS. 249 

2 small bands, 4| inches from the outsides. 

1 harness-buckle, 4 inches from the outsides, with 2 
tongues, of the form of fig. 12. 

Add whatever more may be wanting for the gears, that 
are for giving it motion. 

For a Meal-Elevator 43 Feet high, Strap 3| Inches wide, 
and a Conveyer for two pairs of Stones. 

270 feet of dry pine, or other inch boards; most of them 
llf or 12 inches wide, of any length, that they may 
suit to be dressed for the case boards, as follows: 

86 feet in length, 6| inches wide, for tops and bottoms 
of the cases. 

86 feet in length, 4§ inches wide, for the side boards, 
truly squared at the edges. 

The back board of the conveyer trough 15 inches, bot- 
tom do. 11 inches, and front 13 inches wide. 

Some 2 inch plank for the pulleys and cog-wheel. 

Scantling for conveyers 6 by 6 or 5| by 5§ inches, of 
dry pine or yellow poplar, (prefer light wood;) pine 
for shafts, 4| by A.\ or 5 by 5 inches. 

2^ sides of good, pliant harness leather. 

1500 of 14 ounce tacks. 

A good, clean but of willow for buckets, unless the pieces 
that are left, which are too small for the wheat-buck- 
ets, will make the meal-buckets. 

4 lbs. of 8 penny, and 1 lb. of 10 penny nails. 

2 dozens of large wood screws, (nails will do,) for the 
pulley cases. 

Smith's Bill of Iron. 

1 double gudgeon, (such as fig. 4, Plate VI.,) 1| inch 
thick, 7| inches between the necks, 3^ between the 
key-holes, the necks 1^ inch long, and the tenons at 
each end of the same length, exactly square, that the 
socket may fit every way alike. 

3 sockets, one for each tenon, such as appears on the one 
end of fig. 4. The distance between the outside of 
the straps, with the nails in, must be 5± inches; fig. 
5 is an end view of it, and the band that drives over 



250 BILLS OF MATERIALS. [CHAP. XII. 

it at the end of the shaft, as they appear on the end of 
the conveyer. 

2 small | inch gudgeons for the other ends of the con- 
veyers. 

4 thin bands 5| inches from the outsides, for the con- 
veyers. 

1 gudgeon an inch thick, neck 3f inches, and tang, 10 
inches, for the shaft in the upper pulley; but if a 
gudgeon be put through the pulley, let it be of the 
form of fig. 6, with a tenon and socket at one end, like 
fig. 4. 

1 harness-buckle, 3| inches from the outsides, with two 
tongues; such as fig. 12, Plate VI. 

Add whatever more small gudgeons and bands may be 
necessary for giving motion. 

For a Hopper-Boy. 

1 piece of dry, hard, clean, pine scantling, 4| by 4| 
inches, and 10 feet long, for the upright shaft. 

1 piece of dry poplar, soft pine, or other soft, light wood, 
not subject to crack and split in working, 8 by 2| 
kiches, 15 or 16 feet long, for the flight arms. 

Some two inch plank for wheels, to give it motion, and 
scantling 4f by 4| inches, for the shafts. 

60 flights, 6 inches long, 3 inches wide, and § inch at 
one, and i at the other edge, thinner at the fore than 
hind end, that they may drive in tight like a dove-tail 
wedge. These may be made out of green, hard ma- 
ple, split from sap to heart, and set to dry. 

Half a common bed-cord, for a leading line, and balance 
rope. 

Smith's Bill of Iron. 

1 stay-iron, C F E, Plate VII. fig. 12. The height from 
the top of the ring F, to the bottom of the feet C E, 
is 15 inches; distance of the points of the feet CE, 24 
inches ; size of the legs \ by f inch ; size of the ring F, 
1 by \ inch, round and smooth inside ; 4 inches diame- 
ter, the inside corners rounded off, to keep it from 
cutting the shaft ; there must be two little loops, or 



CHAP. XII.] MILL FOR HULLING RICE, &C 251 

eyes, one in each quarter, that the balance rope may- 
be hung to either. 
2 screws with thumb-nuts, (that are turned by the thumb 

and fingers) £ of an inch thick, and 3 inches long, for 

the feet of the stay-iron. 
2 do. for the end flights, 3| inches long, rounded If inch 

next the head, and square 1| inch next the screw, the 

round part thickest. 
2 do. for the end sweepers, 6% inches long, rounded 1 

inch next the head, J inch thick. 
2 do. for the hopper sweepers, 8| inches long, and | 

inch thick, or long nails, with rivet heads, will answer 

the purpose. 
1 step gudgeon, (fig. 15,) 2| inches long below the ring, 

and tang 9 inches, f inches thick. 
1 plate, 4 by 4, and | inch thick, for the step gudgeon to 

pass through, (fig. 14.) 
1 band for the step-gudgeon, 3| inches diameter; from 

the outside it has to pass through the stay-iron. 
1 gudgeon and band, for the top of the shaft, gudgeon | 

inch, band 4 inches diameter, measuring the outside. 

The smith can, by the book, easily understand how to 
make these irons; and the reader may, from these bills of 
materials, make a rough estimate of the whole expense, 
which he will find trifling, compared with their uti- 
lity. 



article 103. 

A MILL FOR CLEANING AND HULLING RICE. 

Fig. 2, Plate X. The rice brought to the mill in 
boats, is to be emptied into the hopper 1, out of which 
it is conveyed by the conveyer into the elevator at 2, 
which elevates it into the garner 3, on the third floor; 
thence it descends into the garner 4, which hangs over 
the stones 5, and supplies them regularly. The stones 
are to be dressed with a few deep furrows, with but little 
draught, and picked full of large holes; they must be set 



252 MILL FOR HULLING RICE, &C. [CHAP. XII. 

more than the length of the grain apart. The hoop 
should be lined inside with strong sheet-iron, and this, if 
punched full of holes, will be thereby improved. The 
grain is to be kept under the stone as long as necessary : 
this is effected by forcing it to rise some distance up the 
hoop, to be discharged through a hole, which is to be 
raised, or lowered, by a gate sliding in the bottom of it. 
The principle by which the grains are hulled, is that 
of rubbing them against one another, between the stones 
with great force ; by which means they hull one another 
without being much broken by the stones. As the grain 
passes through the stones 5, it should fall into a rolling- 
screen or shaking sieve 6, made of wire, with such 
meshes as will let out all the sand and dust, which may, 
if convenient, run through the floor into the water; the 
rice, and most of the heavy chaff, should fall through into 
the conveyer, which will convey it into the elevator at 
2. The light chaff, &c, that does not pass through the 
sieve, will fall out at the tail, and, if useless, may also run 
into the water and float away. There may be a fan put 
on the spindle, above the trundle, to make a light blast, 
to blow out the chaff and dust, which should be conveyed 
out through the wall, and this fan may supersede the ne- 
cessity of the shaking-sieve. The grain and heavy chaff 
are to be elevated into garner 7; thence they are to de- 
scend into garner 8, and pass through the stones 9, which 
are to be fixed and dressed in the same way as the others, 
but are to rub the grain harder. The outside of the chaff, 
from its sharpness, will cut off all the inside hull from 
the grain, and leave it perfectly clean : as it falls from 
these last stones, it passes through the wind of the fan 
10, fixed on the spindle of the stones 9, which will blow 
out the chaff and dust, and they then drop into the room 
21 ; the wind should escape through the wall. There is 
a regulating board that moves on a joint at 21, so as to 
take all the grain into the conveyer, which will convey 
it into the elevator at 11, which elevates it into the gar- 
ner 12, to pass through the rolling screen 13; this should 
have meshes of three different sizes ; first, to take out the 
dust, which falls into part 17, by itself; secondly, to pass 



CHAP. XII.] MILL FOR HULLING RICE, &C. 253 

the small rice into apartment 16; the whole grains then 
fall into garner 14, perfectly clean, and are drawn into 
barrels at 15. The fan 18 blows out the dust, and lodges 
it in the room 19, and the wind passes out at 20; the head 
rice falls at the tail of the screen, and runs into the hop- 
per of the stones 5, to go through the whole operation 
again. Thus, the whole work is completely performed 
by the water, with the help of the machinery, taking it 
from the boat, and operating upon it until it be put into 
the barrel, without the least manual labour. 

Perhaps it may be advantageous to make a few furrows 
in the edge of the stone, slanting, at an angle of about 30 
degrees with a perpendicular line; these furrows will 
throw up the grain next the stone, on the top of that in 
the hoop, which will change its position continually; but 
this, probably, may not be found necessary. 



PART THE FOURTH. 

On the Process of manufacturing Grain into Flour, as 
practised by the most skilful Millers in the United States. 



CHAPTER XIII. 

ARTICLE 104. 



THE PRINCIPLES OF GRINDING EXPLAINED, TOGETHER WTH SOME OB- 
SERVATIONS ON LAYING OUT THE FURROWS IN THE STONES WITH A 
PROPER DRAUGHT. 

The end we have in view in grinding the grain, is, to 
reduce it to such a degree of fineness, as is found by ex- 
perience to fit it to make the best bread ; and to put it in 
such a state, that the flour may be most effectually se- 
parated from the bran, or skin of the grain, by means of 
sifting or bolting. It has been proved by experience, 
that to grind grain fine with dull mill-stones, will not an- 
swer said purpose, because it kills or destroys that quali- 
ty of the grain, which causes it to ferment and raise in 
the baking; it also makes the meal so clammy, that it 
sticks to the cloth, and chokes up the meshes in bolting; 
hence it appears, that it should be made fine with as lit- 
tle pressure as possible; and it is evident that this can- 
not be done without sharp instruments. Let us suppose 
we undertake to operate on one single grain, it seems to 
accord with reason, that we should first cut it into seve- 
ral pieces, with a sharp instrument, to put it into a state 
suitable for being passed between two planes, in order to 
its being reduced to one regular degree of fineness. The 



256 PRINCIPLES OF GRINDING. [CHAP. XIII. 

planes should have on their faces a number of little sharp 
edges, to scrape off the meal from the bran, and should 
be set at such a distance apart as to reduce the meal to 
the required fineness, and no finer; so that no part can 
escape unground. The same rules or principles will 
apply to any quantity that will serve for one grain. 

To prepare the stones for grinding to the greatest per- 
fection, we may conclude, therefore, that their faces 
must be put into such order, that they will first cut the 
grain into several pieces, and then pass it between them 
in such a manner, that none can escape without being 
ground to a certain degree of fineness, whilst, at the 
same time, it scrapes the meal off cleanly from the bran 
or skin. t 

The best way that I have yet found to effect this, is 
(after the stones are faced with the staff, and pick,) to 
grind between them a few quarts of fine, sharp sand; this 
will face them to fit each other so exactly, that no meal 
can pass them without being ground; this is also the best 
way of sharpening all the little edges on the face, that 
are formed by the pores of the stone; instead of sand, wa- 
ter may be used, the stones then face each other; they 
will then scrape the meal off the bran, without too 
much pressure being applied. But as the meal will not 
pass from the centre to the periphery or verge of the 
stones, with sufficient rapidity, without some assistance, 
there must be a number of furrows, to aid it in its 
egress; and these furrows must be set with such a 
draught that the meal will not pass too far along them at 
once, without passing over the land, or plane, lest it 
should get out unground. They should also be of suffi- 
cient depth, to permit air enough to pass through the 
stones to carry out the heat generated by the friction of 
grinding; but if they have too much draught, they will 
not bear to be deep, or the meal will escape along them 
unground. These furrows ought to be made sharp at the 
feather edge, which is the hinder edge of the furrow, 
and the foremost edge of the land; this serves the pur- 
pose of cutting down the grain; they should be more nu- 
merous near the centre, because there the office of the 



CHAP. XIII.] PRINCIPLES OF GRINDING. 257 

stone is to cut the grain, and near the periphery the of- 
fice of the two planes is to reduce the flour to the re- 
quired fineness, and scrape the bran clean, which is ef- 
fected by the edges formed by the numerous little pores 
with which the burr stone abounds. We must consider, 
however, that it is not best to have the stones too sharp 
near the eye, because they then cut the bran too fine. 
The stones incline to keep open near the eye, unless they 
be too close. If they be porous, (near the eye,) and will 
keep open without picking, they will remain a little dull, 
which will flatten the bran, without cutting it too much : 
but if they be soft next the eye, they will keep too open, 
and that part of the stone will be nearly useless: they, 
therefore, should be very hard and porous. 

It is also necessary that the face of the stone be dressed 
in such a form, as to allow room for the grain, or meal, in 
every stage of its passage between the stones. In order 
to understand this, let us conceive the stream of wheat 
entering the eye of the stone, to be about the thickness 
of a man's finger, but instantly spreading every way 
over the whole face of the stone; this stream must, there- 
fore, get thinner, as it approaches the periphery, where 
it would be thinner than a fine hair, if it did not pass 
slower as it becomes finer, and if the stones were not 
kept apart by the bran ; for this reason the stones must 
be so dressed, that they will not touch at the centre 
within about a 16th or 20th part of an inch, but get 
closer gradually, till within about 10 or 12 inches from 
the verge of the stone, proportioned to the diameter, 
and from that part out they must fit nicely together. 
This close part is called the flouring of the stone. The 
furrows should be deep near the centre, to admit wheat 
in its chopped state, and the air, which tends to keep 
the stones cool. 



17 



258 DRAUGHT OF MILL-STONES. [CHAP. XIII. 



ARTICLE 105. 

OF THE DRAUGHT NECESSARY TO BE GIVEN TO THE FURROWS OF 

MILL-STONES. 

From these principles and ideas, and the laws of cen- 
tral forces, explained at Art. 13, I form my judgment of 
the proper draught of the furrows, and the manner of 
dress; points in which I find but few of the best millers 
to agree; some prefer one kind, and some another, which 
shows that this necessary part of the miller's art is not 
yet well understood. In order to illustrate this matter, 
I have constructed fig. 3, Plate XI. A B represents the 
eight quarter, C D the twelve quarter, and E A the cen- 
tral dress. Now, we observe that in the eight quarter 
dress, the short furrows at F have about five times as 
much draught as the long ones, and cross one another like 
a pair of shears opened so wide that they will drive all be- 
fore them, and cut nothing, and if these furrows be deep, 
they will drive out the meal as soon as it gets into them, 
and thereby make much coarse meal, such as middlings 
and ship stuff or carnel : the twelve quarter dress appears 
to be better; but the short furrows at G have about four 
times as much draught as the long ones, the advantage of 
which I cannot perceive, because if we have once found 
the draught that is right for one furrow, so as to cause 
the meal to pass through the stone in a proper time, it 
appears reasonable that the draught of every other fur- 
row should be equal to it. 

In the central dress E A, the furrows have all one 
draught, and if we could once determine exactly how 
much is necessary, I have no doubt we should find this 
to be the correct plan; and I apprehend that wc shall find 
the best draught to be in a certain proportion to the size 
and velocity of the stone; because the centrifugal force 
that the circular motion of the stone s gives the meal, has 
a tendency to move it outward, and this force will be in 
inverse proportion to the diameter of the stones, their 
velocities being the same: by the fourth law of circular 



CHAP. XIII.] DRAUGHT OF MILL-STONES. 259 

motion. E e is a furrow of the running stone, and we 
may see by the figure, that the furrows cross one ano- 
ther at the centre at a much greater angle than near the 
periphery, which I conceive to be right, because the 
centrifugal force is much less towards the centre than 
near the periphery. But we must also consider, that the 
grain, whole or but little broken, requires less draught and 
centrifugal force to send it out, than it does when ground 
fine ; which shows that we must not, in practice, follow 
the theory laid down in Art. 13, respecting the laws of 
circular motion and central forces; because the grain, as 
it is ground into meal, is less affected by the central force 
to drive it out ; the angles, therefore, with which the 
furrows cross each other, must be greater near the verge 
or skirt of the stone, and less near its centre than would 
be assigned by that theory; and what ought to b3 the 
amount of this variation is a question which practice has 
not yet determined. 

From the whole of my speculations on this difficult sub- 
ject, added to observations on my own and others' prac- 
tice and experience, I propose the following rule for lay- 
ing out a five foot mill-stone. (See fig. 1, Plate XL) 

1. Describe a circle with 3 inches, and another with 6 
inches radius, round the centre of the stone. 

2. Divide the 3 inches space between these two circles 
into 4 spaces, by 3 circles equi-distant; call these five 
circles draught circles. 

3. Divide the stone into 5 parts, by describing 4 circles 
equi-distant between the eye and the verge. 

4. Divide the circumference of the stone into 18 equal 
parts, called quarters. 

5. Then take a straight-edged rule, lay one end at one 
of the quarters at 6, at the verge of the stone, and the 
other end at the outside draught circle, 6 inches from 
the centre of the stone, and draw a line for the furrow 
from the verge of the stone to the circle 5: then shift 
the rule from draught circle 6, to the draught circle 
5, and continue the furrow line towards the centre, 
from circle 5 to 4: then shift in the rule to draught 
circle 4, and continue to 3; shift to 3, and continue to 



260 



DRAUGHT OP MILL-STONES. [CHAP. XIII. 



2; shift to 2, and continue to 1, and the curve of the 

furrow is formed, as 1 — 6 in the figure. 
6. To this curve form a pattern, by which to lay out all 

the remainder. 

The furrows with this curve will cross each other with 
the following angles, shown fig. 1, 
at circle 1, which is the eye 

of the stone, at 75 degrees angle, 

— 2 - 45 

— 3 - - 35 

— 4 - - 31 

— 5 - - 27 

— 6 - - 23 



These angles, as shown bythe lines G r, H r, G s, H s, 
&c, &c, will, I think, do well in practice, will grind 
smooth, and make but little coarse meal, &c. 

Supposing the greatest draught circle to be 6 inches 
radius, then, by theory, the angles would have been 



at circle 1 

2 
3 

4 
5 
6 



138 degrees angle. 

69 

46 

35,5 

27,5 

23 



If the draught circle had been 5 inches radius, and the 
furrows straight, the angles would then have been at 



circle. 



degrees. 



And 6 inches from centre, as shown by 
lines G 1, H 1, 



1 about 180 




— 


110 


2 


— 


60 


3 


— 


38 


4 


— 


29 


5 


— 


23 


6 


— 


18 



Here, the angles near the centre are much too great 
to grind, and they will push the grain before them; to 
remedy this disadvantage, take the aforesaid rule, which 
forms the furrows, as shown at 6 — 7, fig. 1, which is 4 
of 18 qrs. H 8 represents a furrow of the runner, show- 



CHAP. XIII.] DRAUGHT OF MILL-STONES. 261 

ing the angles where they cross those of the bed-stones, 
in every part. Here I have supposed the extremes of the 
draught of 6 inches for the verge, and 3 inches for the 
jeye of the stone, to be right for a stone 5 feet diameter, 
revolving 100 times in a minute; but of this I am, by no 
means, certain. Yet by experience the extremes may be 
ascertained for stones of all sizes, with different velocities; 
no kind of dress of which I can conceive, appears to me 
likely to be brought to perfection excepting this, and it 
certainly appears, both by reason and by inspecting the 
figure, that it will grind the smoothest of all the different 
kinds exhibited in the plate. 

The principle of grinding is partly that of shears, clip- 
ping; the planes of the face of the stones serving as 
guides to keep the grain in the edge of the shears, the 
furrows and pores forming the edges ; if the shears cross 
one another, at too great an angle, they cannot cut; it 
follows, therefore, that all the strokes of the pick should 
be parallel to the furrows. 

To give two stones of different diameters the same 
draught, we must make their draught circles in direct 
proportion to their diameters; then the furrows of the 
upper and lower stones of each size will cross each other 
with equal angles in all proportional distances, from their 
centres to their peripheries. But when we come to con- 
sider that the mean circles of all stones are to have nearly 
equal velocities, and that their centrifugal forces will be 
in inverse proportion to their diameters, we must perceive 
that small stones must have much less draught than large 
ones, in proportion to their diameters. (See the propor- 
tion for determining the draught, Art. 13.) 

It is very necessary that the true draught of the fur- 
rows should be determined to suit the velocity of the 
stone, because the centrifugal force of the meal will varv, 
as the squares of the velocity of the stone, by the 5th law 
of circular motion. But the error of the draught may 
be corrected, in some measure, by the depth of the fur- 
rows. The less the draught, the deeper must be the 
furrow; and the greater the draught, the shallower the 
furrow, to prevent the meal from escaping unground; 



262 OF FACING MILL-STONES. [CHAP. XIII. 

but if the furrows be too shallow, there will not a suffi- 
cient quantity of air pass through the stones to keep them 
cool. But in the central dress the furrows meet so near 
together, that they cut the stones too much away at the 
centre, unless they be made too narrow; T, therefore, pre- 
fer what is called the quarter dress, but divided into so 
many quarters, that there will be little difference between 
the draught of the furrows; suppose 18 quarters in a 5 
foot stone, then each quarter takes up about 10| inches 
of the circumference of the stone, which suits for a divi- 
sion into about 4 furrows and 4 lands, if the stone be 
close; but, if it be open, 2 or 3 furrows to each quarter 
will be enough. This rule will give 4 feet 6 inch stones, 
16; and 5 feet 6 inch stones, 21 ; and 6 feet stones, 23 
quarters. But the number of quarters is not very im- 
portant ; it is better, however, to have too many than too 
few. If the quarters be few, the disadvantage of the short 
furrows crossing at too great an angle, and throwing out 
the meal too coarse, may be remedied by making the 
land widest next the verge, thereby turning the furrows 
toward the centre, when they will have less draught, as 
in the quarter H I, fig. 3. 



ARTICLE 106. 

OF FACING MILL-STONES, 

The burr mill-stones are generally left in such face by 
the maker, that the miller need not spend much labour 
and time on them with picks before he may hang them, 
and grind them together with water or dry sand. After 
they have been ground together for a sufficient length 
of time, they must be taken up, and the red staff tried 
over their faces,* and if it touch in circles, the project- 

* The red staff is made longer than the diameter of the stones, and three inches 
thick on the edge, which is made perfectly straight; on this is rubbed red clay, 
mixed with water, which shows the highest parts of the faces of the stones, when 
rubbed over them, by leaving the red on those high parts. 



CHAP. XIII.] OF FACING MILL-STONES. 263 

ing parts should be well cracked with picks, and again 
ground with a small quantity of water or sand ; after this, 
take them up, and try the staff on them; picking off the 
red parts as before, and repeat this operation, until the 
staff will touch nearly alike all the way across, and until 
the stone comes to a face in eveiy part, that the quality 
thereof may plainly appear; then, with a red or black 
line, proceed to lay out the furrows, in the manner de- 
termined upon, from the observations already laid down 
in the last article. After having a fair view of the face 
and quality of the stone, we can judge of the number of 
furrows most suitable, observing that where the stone is 
most open and porous, fewer furrows will be wanted ; but 
where it is close and smooth, the furrows ought to be 
more numerous, and both they and the lands narrow, 
(about 1| inch wide,) that they may form a greater 
number of edges, to perform the grinding. The fur- 
rows, at the back, should be made nearly the depth of the 
thickness of a grain of wheat, but sloped up to a feather 
edge, not deeper than the thickness of a finger nail;* 
this edge is to be made as sharp as possible, which can 
not be done without a very sharp hard pick. When 
the furrows are all made, try the red staff over them, and 
if it touch near the centre, the marks must be quite taken 
off about a foot next to it, but observing to crack lighter 
the farther from it, so that when the stones are laid to- 
gether, they will not touch at the centre, by about one- 
twentieth part of an inch, and close gradually, so as to 
touch and fit exactly, for about 10 or 12 inches from the 
verge. If the stones be now well hung, having the facing 



* For the form of the bottom of the furrow, see fig. 3, Plate XI. The curve 
line e b shows the bottom, b the feather edge, and e the back part. If the bottom 
had been made square at the back, as at e, the grain would lie in the corner, and 
by the centrifugal force, would work out along the furrows without passing over 
the lands, and a part would escape unground. The back edge must be sloped for 
two reasons; 1st, that the meal may be pushed on to the feather edge; 2dly, that 
the furrow may grow narrower, as the faces of the stones wear away, to give li- 
berty to sharpen the feather edge, without making the furrows too wide. Fig. 5 
represents the face of two stones, working together, the runner moving from a to 
d. When the furrows are just over each other, as at a, there is room for a grain 
of wheat ; when they move to the position of b, it is flattened, and at c, is clipped 
in two by the feather edges and the lands or planes operate on it, as at d. 



264 OF HANGING MILL-STONES. [cHAP. XIII. 

and furrowing neatly done, they will be found in the most 
excellent order that they can possibly be put, for grind- 
ing wheat, because they are in good face, fitting so neatly 
together that the wheat cannot escape unground, and all 
the edges being perfectly sharp, so that the grain can be 
ground into' flour, with the least pressure possible. 



article 107. 



OF HANGING MILL-STONES. 

If the stone have a balance-ryne, it is an easy matter 
to hang it, for we have only to set the spindle perpendi- 
cular to the face of the bed-stone; which is done by fas- 
tening a staff on the cock-head of the spindle, so that the 
end may reach to the edge of the stone, and be near the 
face. In this end we put a piece of elastic material, such 
as of whalebone or quill, so as to touch the stone, that, on 
turning the trundle head, the quill may move round the 
edge of the stone, and when it is made to touch alike all 
the way round, by altering the wedges of the bridge, the 
stone may be laid down and it will be ready hung; # 

* But here we must observe, whether the stone he of a true balance, as it hangs 
on the cock-head, and, if not, it must be truly balanced, by running lead into the 
lightest side. This ought to be carefully attended to by the maker, because the 
stone may be made to balance truly when at rest; yet, if every opposite part do 
not balance each other truly, the stone may be greatly out of balance when in mo- 
tion; and this is the reason why the bush of some stones can be kept tight but a 
few hours, while others will keep so for several months, the spindles being good, 
and the stones balanced when at rest. The reason why a stone that is balanced at 
rest, will sometimes not be balanced in motion, is, that if the upper part be heavi- 
est on one side, and the lower part be heaviest on the other side of the centre, the 
stone may balance at rest, yet, when set in motion, the heaviest parts draw out- 
wards most, by the centrifugal force, which will put the stone out of balance while 
in motion; and if the stone be not round, the parts farthest from the centre will 
have the greatest centrifugal force, because the centrifugal force is as the square 
of the distance from the centre. The neck of the spindle will wear next the long- 
est side, and the bush get loose; and this argues in favour of a stiff ryne. The 
best method that I have seen for hanging stones with stiff horned rynes, is as fol- 
lows : Fix a screw to each horn to regulate by, which is done thus — after the horns 
are bedded, sink under edch horn a strong burr, through which the screw is to 
pass from the neck of the stone, and fasten them in with lead; then, after the stone 
is laid down, put in the screws from the top of the stone, screwing them till the 



CHAP. XIII.] OP HANGING MILL-STONES. 265 

but if we have a stiff ryne, it will be much more difficult, 
because we have not only to fix the spindle perpendicular 
to the face of the bed-stone, but we must set the face of 
the runner perpendicular to the spindle, and all this must 
be done with the greatest exactness, because the ryne, 
being stiff, will not give way to suffer the runner to form 
itself to the bed-stone, as will the balance-ryne. 

The bed of the ryne being first carefully cleaned out, 
the ryne is put into it and tied, until the stone be laid 
down on the cock-head; then we find the part that hangs 
lowest, and, by putting the hand thereon, we press the 
stone down a little, turning it about at the same time, and 
observing whether the lowest part touches the bed-stone 
equally all the way round; if it do not, it is adjusted by 
altering the wedges of the bridge-tree, until it touches 
equally, and then the spindle will stand perpendicular 
to the face of the bed-stone. Then, to set the face of 
the runner perpendicular, or square, to the spindle, we 
remain in the same place, turning the stone, and press- 
ing on it at every horn of the ryne, as it passes, and ob- 
serving whether the runner will touch the bed-stone 
equally at every horn, which, if it do not, we strike 
with an iron bar on the horn, that bears the stone high- 
est, which, by its jarring, will settle itself better into its 
bed, and thereby let the stone down a little in that part; 
but, if this be not sufficient, there must be paper put on 
the top of the horn that lets the stone too low; observing 
to mark the high horns, that when the stone is taken up, 
a little may be taken off the bed, and the ryne will soon 
become so neatly bedded, that the stone will hang very 
easily. But I have always found that every time the 
stone is taken up, the bridge is moved a little out of 
place; or, in other words, the spindle moved a little from 
its true perpendicular position with respect to the face 
of the bed-stone, which is a great objection to the stiff 
horn ryne; for if the spindle be thrown but very little 
out of place, the stones cannot come together equally; 

points bear tightly on the horn: then proceed to hang the stone, which is very 
easily done by turning the screws. 



26G OF REGULATING THE FEED, &C. [CHAP. XIII. 

whilst, with a balance-ryne, if it be considerably out of 
place, it will do but little or no injury in the grinding, 
because the running stone has liberty to form itself to the 
bed-stone. 



ARTICLE 108. 

OF REGULATING THE FEED AND WATER IN GRINDING. 

The stone being well hung, proceed to grind, and when 
all things are ready, draw as much water as is judged to 
be sufficient; then observe fhe motion of the stone, by 
the noise of the damsel, and feel the meal, if it be too 
coarse, and the motion too slow, give less feed, and it will 
grind finer, and the motion will be quicker; if it yet 
grind too coarse, lower the stones; then, if the motion be 
too slow, draw a little more water; but if the meal feel 
to be too low ground, and the motion right, raise the 
stones a little, and give a little more feed. If the motion 
and feed be too great, and the meal be ground too low, 
shut off part of the water. But if the motion be too slow, 
and the feed be too small, draw more water. 

The miller must here remember, that there is a certain 
portion of feed that the stones will bear and grind well, 
which will be in proportion to their size, velocity, and 
sharpness, and, if these be exceeded, there will be a loss, 
as the grinding will not then be well done. But no rule 
can be laid down, to ascertain the proper portion of feed, 
a knowledge depending upon that skill which is only to 
be attained by practice ; as is also the art of judging of 
the right fineness. I will, however, lay down such rules 
and directions as may be of some assistance to the be- 
ginner. 



CHAP. XIII.] OF GOOD GRINDING. 267 

ARTICLE 109. 

RULE FOR JUDGING OF GOOD GRINDING. 

Catch your hand full of meal as it falls from the stones 
and feel it lightly between your fingers and thumb; and 
if it feel smooth, and not oily or clammy, and will not 
stick much to the hand, it shows it to be fine enough, 
and the stones to be sharp. If there be no lumps to be 
felt larger than the rest, but all is of one fineness, it shows 
the stones to be well faced, and the furrows not to have 
too much draught, as none has escaped unground. 

If the meal feel very smooth and oily, and stick much 
to the hand, it shows it to be too low ground, hard 
pressed, and the stones dull. 

If it feel in part oily, and in part coarse and lumpy, and 
•will stick much to the hand, it shows that the stones have 
too much feed; or, that they are dull, and badly faced; 
or have some furrows that have too much draught; or are 
too deep, or perhaps, too steep at the back edge, as part 
has escaped unground, and part is too much pressed, and 
low. 

Catch your hand full, and holding the palm up, shut 
it briskly ; if the greatest quantity of the meal fly out and 
escape between your fingers, it shows it to be in a fine 
and lively state, the stones sharp, the bran thin, and that 
it will bolt well: But the greater the quantity that stays 
in the hand, the more faulty is the flour. 

Catch a handful of meal in a sieve, and sift the meal 
clean out of the bran: then feel it, and if it be soft and 
springy, or elastic, and, also, feel thin, with but little 
sticking to the inside of the bran, and no pieces found 
much thicker than the rest, the stones are shown to be 
sharp, and the grinding well done.* 

* Instead of a sieve, you may take a shovel and hold the point near the stream 
of meal, and it will catch part, of the bran, with but little meal mixed with it; 
which may be separated by tossing it from one hand to the other, wiping the hand 
at each toss. 



268 DRESSING AND SHARPENING, &C. [CHAP. XIII. 

But if it be broad and stiff, and the inside white, it is 
a sure sign that the stones are dull, or over-fed. If you 
find some parts that are much thicker and harder than 
the rest, such as half or quarter grains, it shows that there 
are some furrows that have too much draught, or are too 
deep, or steep, at the back edge; else, that you are grind- 
ing with less feed than the depth of the furrows, and ve- 
locity of the stone will bear. 



ARTICLE 110. 



OF DRESSING AND SHARPENING THE STONES WHEN DULL. 

When the stones get dull they must be taken up, that 
they may be sharpened; to do this in the best manner, 
we must be provided with sharp, hard picks, with which 
the feather-edge of the furrows are to be dressed as sharp 
as possible; which cannot be done with soft or dull picks. 
The bottoms of the furrows are likewise to be dressed, to 
keep them of the proper depth; but here the dull picks 
may be used.* The straight staff must now, also, be run 
over the face carefully, and if there be any parts harder 
or higher than the rest, the red will be left on them; 
they must be cracked lightly, with many cracks, to make 
them wear as fast as the softer parts, in order to keep 
the face good. These cracks also form the edges that 
help to clean the bran ; and the harder and closer the 
stone, the more numerous are they to be. They are to 
be made with a very sharp pick, parallel to the furrows; 
the damper the grain, the more the stone is to be cracked ; 
and the drier and harder it is, the smoother must the 
face be. The hard, smooth places which glaze, may 
be made to wear more evenly, by striking them, either 

* To'prevent the steel from striking your fingers, take a piece of leather about 
. r > by 6 inches square; make a hole through the middle, and put the handle of the 
pick through it, keeping it between your hands and the pick, making a loop in the 
lower edge, through which put one of your fingers, to keep up the lower part from 
the stone. 



CHAP. XIII.] DEGREE OF FINENESS FOR FLOUR. 269 

with a smooth, rough-faced hammer, many light strokes, 
until a dust begins to appear, which frets the flinty part, 
and makes it softer and sharper. The stone will never 
be in the best order for cleaning the bran, without first 
grinding a little sand, to sharpen all the little edges 
formed by the pores of the stone; the same sand may be 
used several times. The stones may be sharpened with- 
out being taken up, or even stopped; to do this, take half 
a pint of sand, and hold the shoe from knocking, to let 
them run empty ; then pour in the sand, and this will 
take the glaze off the face, and whet up the edges so that 
they will grind considerably better: this ought to be often 
done.* 

Some are in the practice of letting stones run for 
months without being dressed; but I am well convinced 
that those who dress them well twice a week, are fully 
paid for their trouble. 



ARTICLE 111. 

OP THE MOST PROPER DEGREE OF FINENESS FOR FLOUR. 

As to the most proper degree of fineness for flour, 
millers differ in their opinion ; but a great majority, and 
many of the most experienced, and of the best judgment, 
agree in this; that if the flour be made very fine, it will 
be killed, (as it is termed,) so that it will not rise or 
ferment so well in baking; but I have heard many good 
millers give it as their opinion, that flour cannot be made 
too fine, if ground with sharp, clean stones, provided 
they be not suffered to rub against each other; and some 
of those millers do actually reduce almost all the meal 
they get out of the wheat into superfine flour; by which 
means they have but two kinds; namely, superfine flour 
and horse-feed; which is what is left after the flour is 

* Care should be taken to prevent the sand from getting mixed with the meal; 
it should be caught in some vessel, the stone being suffered to run quite empty; 
the small quantity that will remain in the stone will not injure the flour. 



270 OF GARLIC, &C. [CHAP. XIV. 

made, and is not fit to make even the coarsest kind of 
ship-bread. 

To test the properties of the finest flour, I contrived to 
catch so much of the dust of that which was floating 
about in the mill, as made a large loaf of bread, which 
was raised with the same yeast, and baked in the same 
oven, with other loaves, that were made out of the most 
lively meal; the loaf made of the dust of the flour was 
equally light, and as good, if not better, than any of the 
others; it was more moist, and pleasant to the taste, 
though made of flour that, from its fineness, felt like oil. 

I conclude, therefore, that it is not the degree of fine- 
ness that destroys the life of the flour, but the degree of 
heat produced by the too great pressure applied in grind- 
ing; and that flour may be reduced to the greatest de- 
gree of fineness, without injuring the quality, provided it 
be done with sharp, clean stones, and with little pressure. 



CHAPTER XIV. 

ARTICLE 112. 

OF GARLIC, WITH DIRECTIONS FOR GRINDING WHEAT MIXED THERE- 
WITH: AND FOR DRESSING THE STONES SUITABLE THERETO. 

In many parts of America there is. a species of onion, 
called garlic, that grows spontaneously with the wheat. 
It bears a head resembling a seed onion, which contains 
a number of grains about the size of a grain of wheat, but 
somewhat lighter.* It is of a glutinous texture, and ad- 

The complete separation of this garlic from the wheat, is so difficult, that it 
has hitherto baffled all our art. Those grains that are larger, and those that are 
smaller than the wheat, can be separated by screens; and those that are much 
lighter, may be blown out by fans ; but those that are of the same size, and nearly 
of the same weight, cannot be separated without putting the wheat in water, 
where the wheat will sink, and the garlic swim. Eut this method is too tedious 
for the miller to practise, except it be once a year, to clean up the headings, rather 
than lose the wheat that is mixed with the garlic, which cannot be otherwise 
sufficiently separated. Great care should be taken by the farmers to prevent this 



CHAP. XIV.] OF GARLIC, &C. 271 

heres to the stone, in such a manner as apparently to 
blunt the edges, so that they will not grind to any degree 
of perfection. We are, therefore, obliged to take the 
runner up, and wash the glaze off with water, scrubbing 
the faces with stiff brushes, and drying up the water with 
cloths or sponges; this laborious operation must be re- 
peated twice, or perhaps four times in 24 hours, if there 
be about ten grains of garlic in a handful of wheat. 

To put the stones in the best order to grind garlicky 
wheat, they must be cracked roughly all over the face, 
and dressed more open about the eye; they then break 
the grains of garlic less suddenly, giving the glutinous 
substance of the garlic more time to incorporate itself 
with the meal, and preventing its adherence to the stone. 
The rougher the face, the longer will the stones grind, 
because the more time will the garlic be in filling all the 
edges. 

The best method that I have ever yet discovered for 
manufacturing garlicky wheat is as follows, namely : — 

First, clean it over several times, in order to take out 
all the garlic that can be separated by the machinery, 
(which is easily done if you have a wheat elevator well 
fixed, as directed in Art. 94, Plate IX.) then chop or 
half grind it; which will break the garlic (it being softer 
than the wheat,) the moisture will then diffuse itself 
through the chopped wheat so that it will not injure the 
stones so much, in the second grinding. By this means 
a considerable quantity can be ground, without taking 
up the stones. The chopping may be done at the rate 
of 15 or 20 bushels in an hour, and with but little trou- 
ble or loss of time, provided there be a meal elevator 
that will hoist it up to the meal loft, from whence it may 
descend to the hopper by spouts, to be ground a second 
time, when it will grind faster than if it had not been 
chopped. Great care should be taken, that it be not 
chopped so fine that it will not feed by the knocking of 
the shoe; as, likewise, that it be not too coarse, lest the 
garlic be not sufficiently broken. If the chopped grain 

troublesome thing from getting root in their farms; which, if it does, it will he 
almost impossible ever to root it out again, as it propagates both by seed and root, 
and is very hardy. 



272 OF GRINDING MIDDLINGS, &C. [cHAP. XV. 

could lie a considerable time, the garlic would dry, and 
it would grind much better. 

But, although every precaution be taken, if there be 
much garlic in the wheat, the bran will not be well 
cleaned; besides which there will be much coarse meal 
made, such as middlings and stuff, which will require to 
be ground over again, in order to make the most profit 
of the grain ; this I shall treat of in the next chapter. 



CHAPTER XV. 

ARTICLE 113. 

OF GRINDING THE MIDDLINGS OVER, AND, IF NECESSARY, THE STUFF 
AND BRAN, OR SHORTS, TO MAKE THE MOST OF THEM. 

Although we may grind the grain in the best manner 
we possibly can, so as to make any reasonable despatch, 
there yet will appear in the bolting, a species of coarse 
meal, called middlings, and stuff, a quality between su- 
perfine and shorts, which will contain a portion of the 
best part of the grain ; but in this state they will make 
very coarse bread, and, consequently, will command but 
a low price. For this reason, it is oftentimes profitable 
to the miller to grind and bolt them over again, and to 
make them into superfine flour, and fine middlings; this 
may easily be done by proper management. 

The middlings are generally hoisted by tubs, and laid 
in a convenient place on the floor in the meal loft, near 
the hopper-boy, until there is a large quantity ga- 
thered: when the first good opportunity offers, it is 
bolted over without any bran or shorts mixed with it, in 
order to take out all that is already fine enough to pass 
through the superfine cloth. The middlings will pass 
through the middling's cloth, and will then be round 
and lively, and in a state fit for grinding, being freed 



CHAP. XV. J OF GRINDING MIDDLINGS. 273 

from the fine part that would have prevented it from 
feeding freely. The small specks of bran that were before 
mixed with it, being lighter than the rich round part, will 
not pass through the middlings' cloth, but will pass on to 
the stuff's cloth. The middlings will, by this means, be 
richer than before, and when made fine, may be mixed 
with the ground meal, and bolted into superfine flour. 

The middlings may now be put into the hanging gar- 
ner, over the hopper of the stones, out of which it will 
run into the hopper, and keep it full, as does the wheat, 
provided the garner be rightly constructed, and a hole 
about 6 by 6 inches made for it to issue out at. There 
must be a rod put through the bar that supports the up- 
per end of the damsel, the lower end of which must reach 
into the eye of the stones, near to the bottom, and on one 
side thereof, to prevent the meal from sticking in the 
eye, which, if it does, it will not feed. The hole in the 
bottom of the hopper must not be less than four inches 
square. Things being thus prepared, and the stones be- 
ing sharp and clean, and nicely hung, draw a small quan- 
tity of water, (for meal does not require above one-tenth 
part that grain does) taking great care to avoid pressure, 
because the bran is not now between two stones, to pre- 
vent their coming too closely together. If you lay on as 
much weight as when grinding grain, the flour will be 
killed ; but if the stones be well hung, and it be pressed 
lightly, the flour will be lively, and will make much bet- 
ter bread, without being bolted, than it would before it 
was ground. As fast as it is ground, it may be elevated 
and bolted; but a little bran will now be necessary to 
keep the cloth open: and all that passed through the su- 
perfine cloth in this operation, may be mixed with what 
passed through in the first bolting of the middlings, and 
be hoisted up, and mixed (by the hopper-boy)«regular]y 
with the ground meal and bolted into superfine flour, as 
directed Art. 89.* 

* All this trouble and loss of time may be saved by a little simple machinery, 
namely: As the middlings fall by the first bolting, let them be conveyed into the 
eye of the stone, and ground with the wheat as directed Art. 89, Plate VIII; by 
which means the whole thereof may be made into superfine flour, without any 
loss of time, or danger of being too hard pressed, for want of bran, to keep the 

18 



274 OF GRINDING MIDDLINGS. [ciIAP. XV* 

The stuff, which is a degree coarser than middlings, if 
it be too poor for ship bread, and too rich to feed cattle 
on, is to be ground over in the same manner as the mid- 
dlings. But if it be mixed with fine flour, (as it some- 
times is,) so that it will not feed freely, it must be bolted 
over first; this will take out the fine flour, and also the 
fine specks of bran, which, being lightest, will come 
through the cloth last. When it is bolted, the part that 
passes through the middlings' and stuff's parts of the 
cloth, are to be mixed and ground together; by this 
means the rich particles will be reduced to flour, and, 
when bolted, will pass through the finer cloths, and will 
make tolerably good bread. What passes through the 
middlings' cloth will make but indifferent ship-bread, and 
what passes through the ship-stuff's cloth, will be what is 
called brown-stuff, roughings, or horse-feed. 

The bran and shorts seldom are worth the trouble of 
grinding over, unless the stones have been very dull, or 
the grinding been but slightly performed, or the wheat 
very garlicky. When it is done, the stones must be very 
sharp, and more water and pressure are required, than in 
grinding grain. The flour, thus obtained, is generally of 
an indifferent quality, being made of that part of the grain 
that lies next the skin, and a great part of it is the skin 
itself, cut fine.* 

stones apart. This mode I first introduced, and several others have since adopt- 
ed it. 

* The merchant miller is to consider, that there is a certain degree of closeness 
or perfection that he is to aim at in manufacturing, which will yield him the great- 
est profit possible, in a given time. And this degree of care and perfection will 
vary with the prices of wheat and flour, so that what would yield the greatest pro- 
fit at one time, would sink money at another; because, if the difference in the price 
of wheat and flour be but little, then we must make the grain yield as much as pos- 
sible, to obtain any profit. But if the price of flour be much above that of the 
wheat, then we had best make the greatest despatch, even if we should not do it 
so well, in order that the greater quantity may be done while these prices last: 
whereas, if we, were to make such a despatch when the price of flour was but little 
above that of wheat, we should sink money. 



CHAP. XVI.] QUALITY OF MILL-STONES, &C. 



275 



CHAPTER XVI. 

ARTICLE 114. 

OF THE QUALITY OF MILL-STONES, TO SUIT THE QUALITY OF THE 

WHEAT. 

It has been found, by experience, that different quali- 
ties of wheat require different qualities of stones, to grind 
to the highest perfection. 

Although there be several species of wheat, of different 



A TABLE 

Showing the Product of a Bushel of Wheat of different weights and qualities, as- 
certained by experiments in grinding parcels. 



D -1 CD_ 

"w m 

CD r» 
CD 


CO 

c 

CD 

a 

CD 

& 

o 

S 

<1 


H 

3 £. 

>— • o 

(ft ^ 

CO P 


CO 

►5" 

CO 

a 
?3 


en 

S3" 
Cfl CD 

G. CO 

a 


3 3 

S" to 

3 P 

era 5 
3. era 

3 CO 

a. 
5'S 

f Si 


o 
o 
IT 5 


Quality of the grain. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


59.5 
59 
60 
61 

56 
59.25 


38.5 
40.23 
38.7 
39.7 

35.81 
35.26 


3.68 
3.65 
3.6 

5.68 

5 
4.4 


2.5 
2.12 
1.16 
2.4 

1.85 

.47 


13.1 
12. 

8.52 
9.54 

7.86 
11.33 


1.72 
I. 

7.57 
3.68 

5.48 
6.79 


59.5 

59. 
60. 
61. 

56. 
59.25 


White wheat, clean. 

Do. do. well cleaned. 
Red do. not well cleaned. 
White do. mixed with green 

garlic. 
White do. very clean. 
Red do. with some cockle 
and light grains. 



If the screenings had been accurately weighed, and the loss in weight occasioned 
by the grinding ascertained, this table would have been more interesting. A loss 
of weight does take place by the evaporation of the moisture by the heat of the 
stones in the operation. 

The author conceived that if a complete separation of the skin of the wheat from 
the flour could be effected, and the flour be reduced to a sufficient degree of fine- 
ness, it might all pass for superfine ; and having made the experiments in the table, 
he effected such improvements in the manufacture, by dressing the mill-stones to 
grind smooth; and by means of the machinery which he invented, returning the 
middlings into the eye of the stone, to be ground over with the wheat, and eleva- 
ting the tail-flour to the hopper-boy, to be bolted over again, &c, that in making 
his last 2000 barrels of superfine flour, he left no middlings or ship-stuff, which 
was not too poor for any kind of bread, excepting some small quantities which 
were retained in the mill; and the flour passed the inspection with credit. Others 
have since pursued the same principles, and put them more fully and completely 
into operation. 



276 QUALITY OF MILL-STONES, &C. [CHAP. XVI. 

qualities; yet, with respect to the grinding, we may 
divide them into three kinds only, namely: — 

1. The dry and hard. 

2. The damp and soft. 

3. Wheat that is mixed with garlic. 

When the grain that is to be ground is dry and hard, 
such as is raised on high and clayey lands, threshed in 
barns, and kept dry,* the stones for grinding it should 
be of that quality of the burr, that is called close and 
hard, with few large pores, in order that they may have 
more face. The grain being brittle and easily broken 
into pieces, requires more face, or plane parts, (spoken 
of in Art. 104,) to reduce it to the required fineness, 
without cutting the skin too much. 

When the grain that is to be ground is somewhat damp 
and soft, such as is raised on a light sandy soil, is trodden 
out on the ground, and is carried in the holds of ships to 
market, which tends to increase the dampness, the stones 
should be more open and porous, because the grain is 
tough, difficult to be broken into pieces, and requires 
more sharp edges, and less face (or plane surface,) to re- 
duce it to the required fineness.! (See Art. 104.) 

When there is garlic or wild onion, (mentioned Art. 
Ill,) mixed with the wheat, the stones require to be 
open, porous, and sharp; because the glutinous substance 
of the garlic adheres to the face of the stones, and blunts 
the edges ; by which means little can be ground before 
the stones get so dull that they will require to be taken 
up and sharpened; and the more porous and sharp the 
stones are, the longer they will run, and grind a larger 
quantity without getting dull. There is a quality of the 
burr stone which may be denominated mellow or soft, 

* Such wheat as is produced hy the mountains and clay lands of the country, 
distant from the sea and tide waters, is generally of a brownish colour, the grain 
appearing flinty, and sometimes the inside a little transparent, when cut by a sharp 
knife. This transparent kind of wheat is generally heavy, and of a thin skin, and 
will make as white flour, and as much of it as the whitest grain. 

f Such is the wheat that is raised in all the low, level, and sandy lands, of coun- 
tries near the sea and tide waters of America, where it is customary to tread out 
their wheat on the ground by horses, and where it sometimes gets wet by rain and 
dew, and the dampness of the ground. This grain is naturally of a fairer colour, 
and softer; and, when broken, the inside is white, which shows it to be nearer to a 
state of pulverization ; it is more easily reduced to flour, and will not bear so much 
pressure as the grain that is raised on high and clay lands; or such that, when 
broken, appears solid and transparent. 



CHAP. XVII.] OF BOLTING REELS AND CLOTH. 277 

to distinguish it from the kind which is hard and flinty; 
these are not so subject to glaze on the face; and it is 
found by experience that stones of this texture will grind 
at one dressing three or four times as much grain mixed 
with garlic, as those of a hard quality.* See Art. 111. 



CHAPTER XVII. 

ARTICLE 115. 

OF BOLTING REELS AND CLOTHS, WITH DIRECTIONS FOR BOLTING 
AND INSPECTING THE FLOUR. 

The effect we wish to produce by sifting, or bolting, 
is to separate the different qualities of flour from each 
other, and from the skin, shorts, or bran; let us now in- 
quire which are the most proper means of attaining this 
end. 

* It is very difficult to convey my ideas of the quality of the stones to the reader, 
for want of something with which to measure or compare their degrees of porosity 
or closeness, hardness or softness. The knowledge of these different qualities is 
only to be attained by practice and experience; but I may observe, that pores in 
the stone, larger in diameter than the length of a grain of wheat, are injurious; 
for how much soever they are larger, is so much loss of the face, because it is the 
edges that do the grinding; therefore all large pores in stones are a disadvantage. 
The greater the number of pores in the stones, so as to leave a sufficient quantity 
of touching surface, to reduce the flour to a sufficient degree of fineness, the better. 

Mill-stone makers ought to be acquainted with the true principles on which 
grinding is performed, and with the art of manufacturing grain into flour, that they 
may be judges of the quality of the stones suitable to the quality of the wheat of 
different parts of the country; also, of the best manner of disposing of the different 
pieces of stone, of different qualities, in the same mill-stone, according to the 
office the several parts, from the centre to the verge of the stone. (See Art. 
104.) 

Mill-stones are generally but very carelessly and slightly made; whereas, they 
should be made with the utmost care, and to the greatest nicety. The runner 
must be balanced exactly on its centre, and every corresponding opposite part of 
it should be of equal weight, or else the spindle will not keep tight in the bush; 
(see Art. 107;) — and if it is to be hung on a balance ryne, it should be put in at 
the formation of the stone, which should be nicely balanced thereon. 

But, above all, the kind of stone should be most attended to, that no piece of an 
unsuitable quality for the rest be put in ; it being known to all experienced millers, 
that they had better give a high price for an extraordinary good pair, than to have 
an indifferent pair for nothing. 



278 OF BOLTING REELS AND CLOTHS. [CHAP. XVII. 



Observations concerning Bolting. 

1. Suppose that we try a sieve, the meshes of which 
are so large, as to let the bran and meal through : It is 
evident that we could never thus attain the end proposed 
by the use thereof. 

2. Suppose we try a finer sieve, that will let all the 
meal through, but none of the bran ; by this we cannot 
separate the different qualities of the flour. 

3. We provide as many sieves of the different degrees 
of fineness as we intend to make different qualities of 
flour; and which, for distinction, we name — Superfine, 
Middlings, and Carnel. , 

The superfine sieve we make of meshes, so fine as to 
let through the superfine flour, but none of the mid- 
dlings: the middlings' sieve, so fine as to let the mid- 
dlings pass through, but none of the carnel: the carnel 
sieve, so fine as to let none of the shorts or bran pass 
through. 

Now it is evident, that if we would continue the ope- 
ration long enough, with each sieve, beginning with the 
superfine, that we might effect a complete separation. 
But if we do not continue the operation a sufficient length 
of time, with each sieve, the separation will not be com- 
plete, for part of the superfine will be left, and will pass 
through with the middlings, and part of the middlings 
with the carnel, and a part of the carnel with the shorts ; 
and this would be a laborious and tedious work, if per- 
formed by hand. 

Many inventions have been made to facilitate this bu- 
siness, amongst which the circular sieve, or bolting reel, 
is one of the foremost; this was, at first, turned and fed 
by hand; and afterwards it was so contrived as to be 
turned by water. But many have been the errors in the 
application of this machine, either from having the cloths 
too coarse, by which means the middlings and small 
pieces of bran passed through with the superfine flour, 
and part of the carnel with the middlings: or by having 
the cloths too short when they are fine enough, so that 
the operation could not be continued a sufficient time to 



CHAP. XVII.] OP INSPECTING FLOUR. 279 

take all the superfine out before it reach the middlings' 
cloth, and all the middlings before it reach the carnel 
cloth. 

The late improvements made on bolting seem to be 
principally as follows, namely: 

1. The using finer cloths — but they were found to clog 
or choke up, when put on small reels of 22 inches dia- 
meter. 

2. The enlarging the diameter of the reels to 27| 
inches, which gives the meal greater distance to fall, and 
causes it to strike harder against the cloth, which keeps 
it open. 

3. The lengthening the cloths, that operation may be 
continued a sufficient length of time. 

4. The bolting a much larger portion of the flour over 
again, than was done formerly. 

The meal, as it is ground, must be hoisted to the meal- 
loft, where it should be spread thin, and often stirred, 
that it may cool and dry, to prepare it for bolting. Af- 
ter it is bolted, the tail flour, or that part of the super- 
fine that falls last, and which is too full of specks of bran 
to pass for superfine, is to be hoisted up again, and mixed 
with the ground meal, to be bolted over again. This 
hoisting, spreading, mixing, and attending the bolting 
hoppers, in merchant mills, creates a great deal of hard 
labour, if performed by hand; and is never completely 
done at last: but all this, and much more of the labour 
of mills, can now be accomplished by machinery, moved 
by water. (See Part III.) 

Of Inspecting Flour. 

The miller must attain a knowledge of the standard 
quality passable in the market: to examine it whilst bolt- 
ing, hold a clean piece of board under the bolt, moving 
it from head to tail, so as to catch a proportional quanti- 
ty all the way, as far as is taken for superfine; then, 
smoothing it well by pressing an even surface on it, will 
make the specks and colour more plainly appear ; if it be 
not good enough, turn a little more of the tail to be bolted 
over. 



2S0 the miller's duty. [chap. XVIII. 

If the flour appear darker than was expected from the 
quality of the grain, it shows the grinding to be too high 
and the bolting too near; because the finer the flour, the 
whiter its colour. 

This proceeding requires a good light; therefore, the 
best way is for the miller to observe to what degree of 
poorness he may reduce his tail flour, of middlings, so as 
to be safe ; by which means he may judge with much 
more safety in the night. But the quality of the tail 
flour, middlings, &c, will greatly vary in different mills; 
for those that have the late improvements for bolting over 
the tail flour, grinding over the middlings, &c, can make 
nearly all into superfine; whereas, in those that have 
them not — the quality that remains next to superfine is 
common or fine flour; then rich middlings, ship stuff", 
&c. Those who have experience will perceive the dif- 
ference in the profits. If the flour feel soft, dead and 
oily, yet is white, it shows the stones to have been dull, 
and too much pressure used. If it appears lively, yet 
dark-coloured, and too full of very fine specks, it shows 
the stones to have been rough and sharp, and that it was 
ground high and bolted too closely. 



CHAPTER XVIIl. 

Directions for keeping the mill, and the business of it, in 

good order. 



ARTICLE 116. 
THE DUTY OF THE MILLER. 

The mill is supposed to be completely finished for 
merchant work, on the new plan; supplied with a stock 
of grain, flour casks, nails, brushes, picks, shovels, scales, 
weights, &c, when the millers enter on their duty. 

If there be two of them capable of standing watch, or 
taking charge of the mill, the time is generally divided 



CHAP. XVIII.] THE MILLER'S DUTY. 28 1 

as follows. In the day-time they both attend to business, 
but one of them has the chief direction. The night is 
divided into two watches, the first of which ends at one 
o'clock in the morning, when the master miller should 
enter on his watch, and continue till day-light, that he 
may be ready to direct other hands to their business ear- 
ly. The first thing he should do, when his watch be- 
gins, is to see whether the stones are grinding, and the 
cloths bolting well. And secondly, he should review 
all the moving gudgeons of the mill, to see whether any 
of them want grease, &c; for want of this, the gudgeons 
often run dry, and heat, which bring on heavy losses in 
time and repairs; for when they heat, they get a little 
loose, and the stones they run on crack, after which they 
cannot be kept cool. He should also see what quantity 
of grain is over the stones, and if there be not enough to 
supply them till morning, set the cleaning machines in 
motion. 

All things being set right, his duty is very easy — he 
has only to see to the machinery, the grinding, and bolt- 
ing once in an hour; he has, therefore, plenty of time to 
amuse himself by reading, or otherwise. 

Early in the morning all the floors should be swept, 
and the flour dust collected; the casks nailed, weighed, 
marked, and branded, and the packing begun, that it 
may be completed in the fore part of the day; by this 
means, should any unforeseen thing occur, there will be 
spare time. Besides, to leave the packing till the after- 
noon, is a lazy practice, and keeps the business out of 
order. 

When the stones are to be sharpened, every thing ne- 
cessary should be prepared before the mill is stopped, 
(especially if there be but one pair of stones to a water- 
wheel) that as little time as possible may be lost: the 
picks should be made quite sharp, and not be less than 
12 in number. Things being ready, the miller is then 
to take up the stone; set one hand to each, and dress 
them as soon as possible, that they may be set to work 
again ; not forgetting to grease the gears and spindle foot. 

In the after part of the day, a sufficient quantity of 
grain is to be cleaned down, to supply the stones the 



282 ACCIDENTS BY FIRE. [CHAP. XVIII. 

whole night; because it is best to have nothing more to 
do in the night, than to attend to the grinding, bolting, 
gudgeons, &c. 



article 117. 

PECULIAR ACCIDENTS BY WHICH MILLS ARE SUBJECT TO CATCH FIRE. 

1. There being many moving parts in a mill, if any 
piece of timber fall, and lie on any moving wheel, or 
shaft, and the velocity and pressure be great, it will gene- 
rate fire, and perhaps consume the mill. 

2. Many people use wooden candlesticks, that may be 
set on a cask, bench, or the floor, and forgetting them, 
the candle burns down, sets the stick, cask, &c, on fire, 
which, perhaps, may not be discovered until the mill is 
in a flame. 

3. Careless millers sometimes stick a candle to a cask, 
or post, and forget it, until it has burnt a hole in the post, 
or set the cask on fire. 

4. Great quantities of grain sometimes bend the floor 
sd as to press the head blocks against the top of the up- 
right shafts, and generate fire, (unless the head blocks 
have room to rise as the flour settles:) mill-wrights should 
consider this, and be careful to guard against it as they 
build. 

5. Branding irons, carelessly laid down, when hot, 
and left, might set a mill on fire. 

6. The foot of the mill-stone spindle, and gudgeons, 
frequently heat, and sometimes set the bridge-tree or shaft 
on fire. It is probable, that, from such causes, mills have 
taken fire, when no person could discover how. 



CHAP. XVIII.] ON IMPROVING MILL-SEATS. 28, 



ARTICLE 118. 

OBSERVATIONS ON IMPROVING MILL-SEATS. 

I may end this part with a few observations on im- 
proving mill-seats. The improvement of a mill-seat at 
a great expense, is an undertaking worthy of mature de- 
liberation, as wrong steps may increase it 10 per centum, 
and the improvement be incomplete: whereas, right steps 
may reduce it 10 per centum, and render them perfect. 

Strange as it may appear, it is yet a real fact, that 
those who have least experience in the milling business, 
frequently build the best and most complete mills. The 
reasons are evident — 

The professional man is bound to old systems, and re- 
lies on his own judgment in laying all his plans; whereas, 
the inexperienced man, being conscious of his deficiency, 
is perfectly free from all prejudice, and is disposed to 
call on all his experienced friends, and to collect all the 
improvements that are extant. 

A merchant w T ho knows but little of the miller's art, 
or of the structure or mechanism of mills is naturally led 
to the following steps; namely: 

He calls several of the most experienced millers and 
mill-wrights, to view the seat separately, and point out 
the spot for the mill-house, dam, &c, and notes their rea- 
sonings. The first, perhaps, fixes on a pretty level spot 
for the mill-house, and a certain rock, that nature seems 
to have prepared to support the breast of the dam, and 
an easy place to dig the race, mill-seat, &c. 

The second passes by these places without noticing 
them; explores the stream to the boundary line; fixes on 
another place the only one he thinks appointed by na- 
ture for building a lasting dam, the foundation a solid 
rock, that cannot be undermined by the tumbling water; 
fixing on a rugged spot for the seat of the house; assign- 
ing for his reasons, that the whole fall must be taken in, 
that all may be right at a future day. He is then in- 
formed of the opinion of the other, against which he gives 
substantial reasons. 



284 OF IMPROVING MILL-SEATS. [cHAP. XVIII. 

The mill-wright, carpenter, and mason, who are to un- 
dertake the building, are now called together, to view the 
seat, fix on the spot for the house, dam, &c. After their 
opinion and reasons are heard, they are informed of the 
opinions and reasons of the others; all are joined toge- 
ther, and the places are fixed on. They are then desired 
to make out a complete draught of the plan for the house, 
&c, and to spare no pains; but to alter and improve on 
paper, till all appear to meet right, in the simplest and 
most convenient manner, (a week may be thus well spent,) 
making out complete bills of every piece of timber, the 
quantity of boards, stone, lime, &c, a bill of iron work, the 
number of wheels, their diameters, number of cogs, &c, 
&c, and every thing else required in the whole work. 
Each person can then make out his charge, and the costs 
can be very nearly counted. Every species of materials 
may be contracted for, to be delivered in due time: the 
work then goes on regularly without disappointment ; 
and when done, the improvements are completes and a 
considerable sum of money saved. 



PART THE FIFTH. 



CHAPTER XIX. 



Practical Instructions for building Mills, with all their pro- 
portions, suitable to all falls, of from three to thirty-six 
feet. Received from Thomas Ellicott, Mill-wright. 



PREFATORY REMARKS. 



This part, as appears from the heading, was written 
by Mr. Thomas Ellicott; a part of his preface, published 
in the early editions of this work, it has been thought 
best to omit. After some remarks upon the defective 
operation of mills upon the old construction, he proceeds 
to say — 

In the new way, all these inconveniences and disad- 
vantages are completely provided against: (See Plate 
XXII.,) which is a representation of the machinery, as ap- 
plied in the whole process of the manufacture; taking the 
grain from the ship or wagon, and passing it through the 
whole process by water, until it is completely manufac- 
tured into superfine flour. This is a mill of my planning 
and draughting, now in actual practice, built on Occo- 
quam river, in Virginia, with 3 water wheels, and 6 pairs 
of stones. 

If the wheat come by water to the mill, in the ship Z, 
it is measured and poured into the hopper A, and thence 
conveyed into the elevator at B, which elevates it, and 
drops it it into the conveyer C D, which conveys it along 
under the joists of the second floor, and drops it into the 
hopper garner at D, out of which it is conveyed into the 



286 TO THE READER. [CHAP. XIX. 

main wheat elevator at E, which carries it up in the 
peak of the roof, and delivers it into the rolling-screen 
at F, which (in this plan) is above the collar beams, out 
of which it falls into the hopper G, thence into the short 
elevator at H, which conveys it up into the fan I, from 
whence it runs down slanting, into the middle of the long 
conveyer at J, that runs towards both ends of the mill, 
and conveys the grain, as cleaned, into any garner 
K K K K K K, over all the stones, which is done by shift- 
ing a board under the fan, to guide the grain to either 
side of the cog-wheel J; and although each of these gar- 
ners should contain 2000 bushels of wheat, over each pair 
of stones 12000 bushels in 6 garners, yet nearly all may 
be ground out without handling it, and the feed of the 
stones will be more even and regular than is possible in 
the old way. As it is ground by the several pairs of 
stones, the meal falls into the conveyer at M M M, and 
is conveyed into the common meal elevator at N, which 
raises it to O; from thence it runs down the hopper-boy 
at P, which spreads and cools it over a circle of 10 or 
15 feet diameter, and (if thought best) will rise over it, 
and form a heap two or three feet high, perhaps thirty 
barrels of flour, or more at a time, which may be bolted 
down at pleasure. When it is bolting, the hopper-boy 
gathers it into the bolting hoppers atQ, and attends them 
more regularly than is ever done by hand. As it is bolt- 
ed, the conveyer R, in the bottom of the superfine chest, 
conveys the superfine flour to a hole through the floor at 
S, into the packing chest, which mixes it completely. 
Out of the packing chest it is filled into the barrel at T, 
weighed in the scale U, packed at W by water, headed 
at X, and rolled to the door Y, then lowered down by a 
rope and windlass, into the ship again at Z. 

If the wheat come to the mill by land, in the wagon 7, 
it is emptied from the bags into a spout that is in the wall, 
and it runs into the scale S, which is large enough to hold 
a wagon load; and as it is weighed it is (by drawing a 
gate at bottom) let run into the garner D, out of which it 
is conveyed into the elevator at E, and so through the 
same process as before. 



CHAP. XIX.] TO THE READER. 287 

As much of the tail of the superfine reels 37 as we 
think will pass inspection, we suffer to pass on into the 
short elevator, (by shutting the gates at the bottom of the 
conveyer next the elevator, and opening one farther to- 
wards the other end.) The rubblings, which fall at the 
tail of said reels, are also hoisted into the bolting hoppers 
of the sifting reel 39, which is covered with a fine cloth, 
to take out all the fine flour dust, which will stick to the 
bran in warm damp weather; and all that passes through 
it is conveyed by the conveyer 40, into the elevator 41, 
which elevates it so high that it will run freely into the 
hopper-boy at O; and is bolted over again with the 
ground meal. The rubblings, that fall at the tail of the 
sifting reel 39, fall into the hopper of the middlings' reel 
42 ; and the bran falls at the tail into the lower story. 
Thus, you have it in your power, either by day or night, 
without any hand labour, except to shift the sliders, or 
some such trifle, to make your flour to suit the standard 
quality ; and the greatest possible quantity of superfine 
is made out of the grain, and finished completely at one 
operation. 

Agreeably to request, I shall now attempt to show the 
method of making and putting water on the several kinds 
of water wheels commonly used, with their dimensions, 
&c, suited to falls and heads of from 3 to 36 feet. I 
have also calculated tables for gearing them to mill-stones; 
and made draughts* of several water wheels with their 
forebays, and manner of putting on the water, &c. 

THOiVIAS ELLICOTT. 



* All my draughts are taken from a scale of eight feet to an inch, except Plate 
XVII., which is four feet to an inch. 



288 OF UNDERSHOT MILLS. [CHAP. XIX. 



ARTICLE 119. 

OF UNDERSHOT MILLS. 

Fig. 1, Plate XIII., represents an undershot wheel, 18 
feet diameter, with 3 feet total head and fall. It should 
be two feet wide for every foot the mill-stones are in di- 
ameter; that is, 8 feet between the shrouds for a 4 feet, 
and 10 feet wide for a 5 feet stone. It should have three 
sets of arms and shrouds, on account of its great width. 
Its shaft should be at least 26 inches in diameter. It re- 
quires 12 arms, 18 feet long, 3§ inches thick, by 9 wide; 
and 24 shrouds, 7| feet long, 10 inches deep, by 3 thick, 
and 32 floats, 15 inches wide. Note — It may be geared 
the same as an overshot wheel, of equal diameter. Fig. 
2 represents the forebay, with its sills, posts, sluice, and 
fall: I have, in this case, allowed 1 foot fall and 2 feet 
head. 

Fig. 3 represents an undershot wheel, 18 feet diame- 
ter, with 7 feet head and fall. It should be as wide be- 
tween the shrouds as the stone is in diameter ; its shaft 
sfiould be 2 feet in diameter; requires 8 arms, 18 feet 
long, 3| inches thick, by 9 wide ; and 16 shrouds, 7§ feet 
long, 10 inches deep, by 3 thick. It may be geared the 
same as an overshot wheel 13 feet in diameter, because 
their revolutions per minute will be nearly equal. 

Fig. 4 represents the forebay, sluice, and fall ; the head 
and fall about equal. 

Fig. 5 represents an undershot wheel, 12 feet diame- 
ter, with 15 feet total head and fall. It should be 6 
inches wide for every foot the stone is in diameter. Its 
shaft 20 inches in diameter; requires 6 arms, 12 feet 
long, 3 by 8 inches; and 12 shrouds, 6| feet long, 2| 
inches thick, and 8 deep. It suits well to be geared to 
a 5 feet stone with single gears, 60 cogs in the cog- 
wheel, and 16 rounds in the trundle; to a 4| feet stone, 
with 62 cogs and 15 rounds; and, to a 4 feet stone with 
64 cogs and 14 rounds. These gears will do well till the 
fall is reduced to 12 feet, only the wheel must be less, as 



CHAP. XIX.] OF UNDERSHOT MILLS. 289 

the falls are less so as to make the same number of revo- 
lutions in a minute; but this wheel requires more water 
than a breast-mill with the same fall. 

Fig. 6 is the forebay, gate, shute, and fall. Forebays 
should be wide, in proportion to the quantity of water 
they are to convey to the wheels, and should stand 8 or 
10 feet in the bank, and be firmly joined, to prevent the 
water from breaking through ; which it will certainly do, 
unless they be well secured. 



article 120. 

DIRECTIONS FOR MAKING FOREBAYS. 

The best way with which I am acquainted, for making 
this kind of forebays, is shown in Plate XVII., fig. 7. 
Make a number of solid frames, each consisting of a sill, 
two posts, and a cap; set them cross-wise, (as shown in 
the figure,) 2| or 3 feet apart; to these the planks are to 
be spiked, for there should be no sills lengthwise, as the 
water is apt to find its way along them. The frame at 
the head next the water, and one 6 or 8 feet downwards 
in the bank, should extend 4 or 5 feet on each side of the 
forebay into the bank, and be planked in front, to pre- 
vent the water and vermin from working round. Both 
of the sills of these long frames should be well secured, 
by driving down plank, edge to edge, like piles, along 
the upper side, from end to end. 

The sills being settled on good foundations, the earth 
or gravel must be rammed well on all sides, full to the 
top of the sills. Then lay the bottom with good, sound 
plank, well jointed and spiked to the sills. Lay your 
shute, extending the upper end a little above the point 
of the gate when full drawn, to guide the water in a right 
direction to the wheel. Plank the head to its proper 
height, minding to leave a suitable sluice to guide the 
water smoothly down. Fix the gate in an upright posi- 
tion — hang the wheel, and finish it off, ready for letting 
on the water. 
19 



290 OP UNDERSHOT MILLS. [CHAP. XIX, 

A rack must be made across the stream, to keep off the 
floating matter that would break the floats and buckets 
of undershot, breast, and pitch-back wheels, and injure 
the gates. (See at the head of the forebay, fig. 7, Plate 
XVII.) This is done by setting a frame 3 feet in front 
of the forebay, and laying a sill 2 feet in front of it, for the 
bottom of the rack; in it the staves are put, made of laths, 
set edgewise with the stream, 2 inches apart, their upper 
ends nailed to the cap of the last frame; which causes 
them to lean down stream. The bottom of the race must 
be planked between the forebay and rack, to prevent the 
water from making a hole by tumbling through the rack 
when choked; and the sides must be planked outside of 
the post to keep up the bank,s. This rack must be twice 
as long as the forebay is wide, or else the water will not 
come fast enough through it to keep the head up; for the 
head is the spring of motion of an undershot mill. 



article 121. 

ON THE PRINCIPLE OF UNDERSHOT MILLS. 

They differ from all others in principle, because the 
water loses all its force by the first stroke against the 
floats; and the time this force is spending, is in propor- 
tion to the difference of the velocities of the wheel and 
the water, and the distance of the floats. Other mills 
have the weight of the water after the force of the head 
is spent, and will continue to move; but an undershot 
will stop as soon as the head is spent, as they depend 
not on the weight. They should be geared so, that when 
the stone goes with a proper motion, the water-wheel 
will not run too fast, as they will not then receive the 
full force of the water; nor too slow, so as to lose its power 
by its rebounding and dashing over the buckets. This 
matter requires very close attention, and to find it out by 
theory, has puzzled our mechanical philosophers. They 
give us for a rule, that the wheel must move just one- 
third the velocity of the water: perhaps this may suit 



CHAP. XIX.] OF UNDERSHOT MILLS. 291 

where the head is not much higher than the float-boards; 
but I am fully convinced that it will not suit high heads. 



Experiments for determining the proper Motion for 
Undershot Wheels. 

I drew a full sluice of water on an undershot wheel 
with 15 feet head and fall, and counted its revolutions 
per minute; then geared it to a mill-stone, set it to work 
properly, and again counted its revolutions, and the dif- 
ference was not more than one-fourth slower. I believe, 
that if I had checked the motion of the wheel to be equal 
to one-third the motion of the water, the water would 
have rebounded and flown up to the shaft. Hence, I 
conclude, that the motion of the water must not be 
checked by the wheel more than one-third, nor less than 
one-fourth, else it will lose in power; for, although the 
wheel will carry a greater load with a slow, than with a 
swift motion, yet it will not produce so great an effect, 
its motion being too slow. And again, if the motion be 
too swift, the load or resistance it will overcome will be 
so much less, that its effect will be lessened also. I con- 
clude, that about two-thirds the velocity of the water is 
the proper motion for undershot wheels; the water will 
then spend all its force in the distance of two float-boards. 
It will be seen that I differ greatly with those learned 
authors who have concluded that the velocity of the 
wheel ought to be but one-third of that of the water. To 
confute them, suppose the floats 12 inches, and the co- 
lumn of water striking them, 8 inches deep; then, if two- 
thirds of the motion of this column be checked, it must 
instantly become 24 inches deep, and rebound against 
the backs of the floats, and the wheel would be wallow- 
ing in this dead water; whereas, when only one-third of 
its motion is checked, it becomes 12 inches deep, and 
runs off from the wheel in a smooth and lively manner. 



292 



OF UNDERSHOT WHEELS. 



[chap. XIX. 



Directions for gearing Undershot wheels, 18 feet in diameter, 
where the head is above 3 and tender 8 feet, with double 
gears ; counting the head from the point ivhere the water 
strikes the floats. 

1. For 3 feet head and 18 feet wheel, see 18 feet wheel 
in the overshot table. 

2. For 3 feet 8 inches head, see 17 feet wheel in do. 

3. For 4 feet 4 inches head, see 16 feet wheel in do. 

4. For 5 feet head, see 15 feet wheel in do. 

5. For 5 feet 8 inches head, see 14 feet wheel in do. 

6. For 6 feet 4 inches head, see 13 feet wheel in do. 

7. For 7 feet head, see 12 feet wheel in do. 

The revolutions of the wheels will be nearly equal; 
therefore the gears may be the same. 

The following table is calculated to suit for any sized 
stone, from 4 to 6 feet diameter, different sized water- 
wheels from 12 to 18 feet diameter, and different heads 
from 8 to 20 feet above the point it strikes the floats ; 
and to make 5 feet stones revolve 88 times; 4 feet 6 inch 
stones 97 times; and 4 feet stones 106 times in a minute, 
when the water-wheel moves two-thirds the velocity of 
the striking water. 

MILL-WRIGHTS' TABLE FOR UNDERSHOT MILLS, SINGLE GEAR. 



I % 

CD o 


CD | 

^ 2 

CD ** 


Velocity 
ter per 
feet. 


Velocity 
ter-whee 
nute in 


uevolutio 

stone pi 

Revolutio 

water- wl 

nute. 


!2 

p 
3 

§2 


2 

ST CD 

3 o 


Uevolutio 
mill-ston 
the wate 


CD 
1 ^ CD 

3 - "' 


5' g. 

_, fD 

CD — 
f CD 

C 

o 


2-o 
5' ,_. 

CD 1 CD 


o 

3 "" 

rf CD 
CD 


?y~ o 

CD 3" 
-! CD 

3 3 


CD co 
Q 

*v 2, 

CD 
*-t 

T a> 


-» TO 

3 
5°° 

CD 
CD 


5' 

CD 


CD t-j 
C 

CD B 

B- TO 

5" 


7 CD 3 

k ^ 

CD "* O 
CD_ o ,_ *l 
TO ^ 
• CO 

2,c? 


CD 

CD E^ 

V CD 

TO 
O 

B 

CD 
TO 


8 


12 


1360 


906 


24 


88 


56 


15 


3| 


5 


9 


13 


1448 


965 


23 i 


88 


58 


15 


3* 


5 


10 


14 


1521 


1014 


23^ 


88 


58 


15 


3f 


5 


11 


15 


1595 


1061 


22 J 


88 


58 


15 


3f 


5 


12 


16 


1666 


1111 


22i 


88 


58 


15 


3* 


5 


13 


16 


1735 


1157 


231 


88 


60 


16 


3| 


5 


14 


16 


1800 


1200 


24 


88 


59 


16 




5 


15 


16 


1863 


1242 


24f 


88 


60 


17 


34 


5 


16 


16 


1924 


1283 


25# 


88 


59 


17 


3 f 


5 


17 


17 


1983 


1322 


25 


88 


62 


17 


3# 


5 


IS 


17 


2041 


1361 


25| 


88 


62 


17 


3f 


5 


19 


18 


2097 


1398 


25 


88 


62 


17 


3* 


5 


20 


18 


2152 


1435 


25£ 


88 


60 


17 




5 


1 | 


2 


3 


4 


5 | 6 


7 


8 


9 1 


10 



CHAP. XIX.] OF BREAST WHEELS. 293 

Note that there are nearly 60 cogs in the cog-wheel, 
in the foregoing table, and 60 inches is the diameter of 
a 5 feet stone: therefore it will do, without sensible er- 
ror, to put one cog more in the wheel for every inch that 
the stone is less than 60 inches diameter, down to 4 feet; 
the trundle head and water wheel remaining the same; 
and for every three inches that the stone is larger than 
60 inches in diameter, put 1 round more in the trundle, 
and the motion of the stone will be nearly right up to 6 
feet diameter. 



article 122. 

OF BREAST WHEELS. 

Breast wheels differ but little in their structure or mo- 
tion from overshot, excepting, only, that the water passes 
under instead of over them, and they must be wider in 
proportion as their fall is less. 

Fig. 1, Plate XIV., represents a low breast with 8 feet 
head and fall. It should be 9 inches wide for every foot 
of the diameter of the stone. Such wheels are generally 
IS feet diameter; the number and dimensions of their 
parts being as follows: 8 arms 18 feet long, 3£ by 9 
inches; 16 shrouds 8 feet long, 2§ by 9 inches; 56 buck- 
ets ; and shaft, 2 feet diameter. 

Fig. 2 shows the forebay, water-gate, and fall, and 
manner of striking on the water. 

Fig. 3 is a middling breast wheel, 18 feet diameter, 
with 12 feet head and fall. It should be 8 inches wide 
for every foot the stone is in diameter. 

Fig. 4 shows the forebay, gate, and fall, and manner of 
striking on the water. 

Fig. 5 and 6, is a high breast wheel, 16 feet diameter, 
with 3 feet head in the forebay, and 10 feet fall. It 
should be 7 inches wide for every foot the stone is in dia- 
meter. The number and dimensions of its parts are 6 
arms, 16 feet long, 3| by 9 inches; 12 shrouds, 8 feet 6 
inches long, 2| by 8 or 9 inches deep, and 48 buckets. 



294 OF PITCH-BACK WHEELS. [CHAP. XIX. 



ARTICLE 123. 

OF PITCH-BACK WHEELS. 

Pitch-back wheels are constructed exactly similar to 
breast wheels, only the water is struck on them at a 
greater height. Fig. 1, Plate XV., is a wheel 18 feet 
diameter, with 3 feet head in the penstock, and 16 feet 
fall below' it. Should be 6 inches wide for every foot 
of the diameter of the stone. 

Fig. 2 shows the trunk, penstock, gate, and fall; the 
gate sliding on the bottom of the penstock, and drawn by 
the lever A, turning on the roller. This wheel is much 
recommended by some mechanical philosophers, for the 
saving of water; but I do not join them in opinion, but 
think that an overshot with an equal head and fall, is 
fully equal to it in power; besides the saving of the ex- 
pense in building so high a wheel, and the greater diffi- 
culty of keeping it in order.* 



ARTICLE 124. 

OF OVERSHOT "WHEELS. 

Overshot wheels receive their water on the top, being 
moved by its weight ; and are much to be recommended 
where there is fall enough for them. Fig. 3 represents 
one, 18 feet diameter, which should be about 6 inches 
wide for every foot the stone is in diameter. It should 
hang 8 or 9 inches clear of the tail water, otherwise the 
water will be drawn back under it. The head in the 
penstock should be generally about 3 feet, which will 
spout the water about one-third faster than the wheel 
moves. Let the abate have about 3 inches fall, and di- 
rect the water into the wheel at the centre of its top. 

I have calculated a table for gearing overshot wheels, 
which will suit equally well any of the others of equal 
diameter, that have equal heads above the point where 
the water strikes the wheel. 

* On this subject see the Appendix. — Editoe. 



CHAP. XX.] OF OVERSHOT WHEELS. 295 

Dimensions of this wheel, 8 arms, 18 feet long, 3 by 9 
inches; 16 shrouds 7 feet 9 inches long, 2§ by 7 or 8 
inches; 56 buckets; and shaft 24 inches diameter. 

Fig. 4 represents the penstock and trunk, &c, the wa- 
ter being let on the wheel by drawing the gate G. 

Fig. 1 and 2, Plate XVI., represents a low overshot, 
12 feet diameter, which should be in width equal to the 
diameter of the stone. Its parts and dimensions are, 6 
arms 12 feet long, 3| by 9 inches; 12 shrouds 6§ feet 
long, 2| by 8 inches ; shaft 22 inches diameter, and 30 
buckets. 

Fig. 3 represents a very high overshot, 30 feet diame- 
ter, which should be 3§ inches wide for every foot of the 
diameter of the stone. Its parts and dimensions are, 6 
main arms, 30 feet long, 3i inches thick, 10 inches wide 
at the shaft, and 6 at the end ; 12 short arms, 14 feet long, 
of equal dimensions; which are framed into the main 
arms near the shaft, as in the figure, for if they were all 
put through the shaft, they would make it too weak. 
The shaft should be 27 inches diameter, the whole being 
very heavy, and bearing a great load. Such high wheels 
require but little water. 



CHAPTER XX. 

ARTICLE 125. 

OF THE MOTION OF OVERSHOT WHEELS. 

After trying many experiments, I conclude that the 
circumference of overshot wheels geared to mill-stones, 
grinding to the best advantage, should move 550 feet in 
a minute; and that of the stones 1375 feet in the same 
time: that is, while the wheel moves 12, the stone moves 
30 inches, or in the proportion of 2 to 5. 

Then, to find how often the wheel we propose tp make, 
will revolve in a minute, take the following steps: 1st, 
Find the circumference of the wheel by multiplying the 
diameter by 22, and dividing by 7, thus: 



296 OF GEARING. [CHAP. XX. 

Suppose the diameter to be 16 feet,") ^ 

then, 16 multiplied by 22, produces 352, I 
which, divided by 7, gives 50 2-7 for the f 
circumference. J 



32 
32 



7)352 
50 2-7 



By which we divide 550, the dis-"| 
tance the wheel moves in a minute, j 50 n 55) o 
and it gives 11, for the revolutions of y 
the wheel per minute, casting off the | 
fraction 2-7, it being small. J 



11 times. 



To find the revolutions of the stone"] 54 



22 



per minute, 4 feet 6 inches (or 54 | 
inches) diameter, multiply 54 inches V ios 
by 22, and divide by 7, and it gives 169 | ]^__ 
5-7 (say 170) inches, the circumference J 7)ii88 
of the stone. 



169 5-7 



By which divide 1375 feet, or 16500^| 1375 



12 



inches, the distance the skirt of the 1 

stone should move in a minute, and it 1 i7|0)i650,o(97 

gives 97 ; the revolution of a stone per f 

minute, 4| feet diameter. j 120 

j 

To find how often the stone revolves "| 
for once of the water-wheel, divide 97, j 
the revolutions of the stone, by 11, the y 
revolutions of the wheel, and it gives 8 j 
9-11, (say 9 times.) J 



119 



11)97 

8 9-11 



ARTICLE 126. 
OF GEARING. 

If the mill were to be single-geared, 99 cogs and 11 
rounds would give the stone the right motion, but the 
cog-wheel would then be too large, and the trundle too 
small ; it must, therefore, be double-geared. 



CHAP. XX.] 



OF GEARING. 



29' 



Suppose we choose 66 cogs in the big • 
cog-wheel and 48 in the little one, and 
25 rounds in the wallower, and 15 in 
the trundle. 

Then to find the revolutions of the 
stone for one of the water-wheels, mul- [> 
tiply the cog-wheels together, and the 
wallower and trundle together, and di- 
vide one product by the other, and it 
will give the answer, 84-41? not quite 8§ 
revolutions, instead of 9. 



25 
15 

1-25 
25 

375 



66 

48 

528 
264 

375)3168(8 168-375 
3000 

168 



We must, therefore, devise another proportion — Con- 
sidering which of the wheels we had best alter, and wish- 
ing not to alter the big cog-wheel or trundle, we put one 
round less in the wallower, and two cogs more in the lit- 
tle cog-wheel, and multiplying and dividing as before, 
we find the stone will turn 9| times for once of the wa- 
ter-wheel, which is as near as we can get. The mill now 
stands thus, a 16 feet overshot wheel, that will revolve 
1 1 times in a minute, geared to a stone 4§ feet in diame- 
ter; the big cog-wheel 66 cogs, 4§ inches from centre to 
centre of the cogs; (which we call the pitch of the gear) 
little cog-wheel 50 cogs 4| pitch; wallower 24 rounds, 
4 1 pitch j and trundle 15 rounds, 4| inches pitch. 

article 127. 



RULES FOR FINDING THE DIAMETER OF THE PITCH CIRCLES. 

66 



To find the diameter of the pitch "* 
circle that the cogs stand in, multiply 
the number of cogs by the pitch, which 
gives the circumference; this multi- } 
plied by 7, and divided by 22 gives the 
diameter in inches; which, divided by 
12, reduces it to feet and inches; thus: 



264 
33 

297 
7 

22)2079(94J 

198 

99 



11 



298 RULES FOR FINDING THE DIAMETER, &C, [CHAP. XX. 

For the cog-wheel of 66 cogs; and 4| inches pitch, we 
find 7 feet 10§ inches to be the diameter of the pitch cir- 
cle; to which I add 8 inches for the outside of the cogs, 
which makes 8 feet 6| inches, the diameter from out to 
out. 

By the same rules, I find the diameters of the pitch 
circles of the other wheels to be as follows ; namely : — 

Little cog-wheel 50 cogs, 4| ) 7J .» pitch cir . 

inches pitch, ) 2 22 r 

I add, for the outside of the circle, ?.£ 



Total diameter from out to out, 6 
Wallower 24 rounds, 4| inches 

pitch, 
Add, for outsides, 3|| do 



2 ll| ,\ do 



Total diameter from the outsides, 3 

Trundle head 15 rounds, 4| ) , ' 3 , 

inches pitch, £ ? ¥ * 

Add, for outsides, 2£ 



11 

'2 2 2 



Total diameter for the outsides, 1 11 

Thus, we have completed the calculations for one mil], 
with a 16 feet overshot water-wheel, and stones 4§ feet 
diameter. By the same rules we may calculate for 
wheels of all sizes from 12 to 30 feet, and stones from 4 
to 6 feet diameter, and may form tables that will be of 
great use even to master workmen, in despatching of bu- 
siness, in laying out work for their apprentices and other 
hands, in getting out timber, &c; but more especially to 
those who are not sufficiently skilled in arithmetic to 
make the calculations. I have from long experience been 
sensible of the need of such tables, and have therefore 
undertaken the task of preparing them. 



CHAP. XX.] EXPLANATION OF THE TABLES. 299 

ARTICLE 128. 

MILL-WRIGHTS' TABLES. 

Calculated to suit overshot water-wheels with suitable 
heads above them, of all sizes, from 12 to 30 feet diame- 
ter, the velocity of their circumferences being about 550 
feet per minute, showing the number of cogs and rounds 
in all the wheels, double gear, to give the circumference 
of the stone a velocity of 1375 feet per minute, also the 
diameter of their pitch circles, the diameter of the out- 
sides, and revolutions of the water-wheel, and stones per 
minute. 

For particulars, see what is written over the head of 
each table. Table I. is to suit a 4 feet stone, Table II. 
a 4|, Table III. a 5 feet, and Table IV. a 5| feet stone. 

N. B. If the stones should be an inch or two larger or 
less than those above described, make use of the table 
that comes the nearest to it, and likewise for the water- 
wheels. For farther particulars see " Draughting Mills." 

Use of the following Tables. 

Having levelled your mill-seat, and found the total fall, 
after making due allowances for the fall in the races, and 
below the wheel, suppose there be 21 feet 9 inches, and 
the mill stones be 4 feet in diameter, then look in Table 
I. (which is for 4 feet stones,) column 2, for the fall that 
is nearest yours, and you find it in the 7th example; and 
against it, in column 8, is 3 feet, the head proper to be 
above the wheel; in column 4 is 18 feet, for the diameter 
of the wheel, &c, for all the proportions of the gears to 
make a steady-moving mill; the stones to revolve 106 
times in a minute.* 

* The following tables are calculated to give the stones the revolution per minute 
mentioned in them, as near as any suitable number of cogs and rounds would per- 
mit, which motion I find is 8 or 10 revolutions per minute slower than proposed 
by Evans, in his table; — his motion may do best in cases where there is plenty 
of power, and steady work on one kind of grain; but, in country mills, where they 
are continually changing from one kind to another, and often starting and stopping, 
I presume a slow motion will work most regularly. His table being calculated 
for only one size of mill-stones, and mine for four, any one choosing his motion, 
may look for the width of the water-wheel, number of cogs and rounds, and size 
of the wheels to suit them, in the next example following, keeping to my table in 
other respects, and you will have his motion nearly. 



300 



TABLES, &C. 



TABLE I. — For Overshot Mills with Stones 4 feet diameter, to revolve 106 
times in a minute, pitch of the gear of the great cog-wheel and wallower* 
4^ inches, and of lesser cog-wheel and trundle 4£ inches. 





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ft. in. 


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feet. 


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ft. in. 




1 


15 3 


2 6 


12 


3 


C66 
1 48 


7 10, 5 

5 4.87 


8 6. 5 
6 0. 5 


25 
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12.5 


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8 2.33 
5 4.87 


8 10.33 
6 0. 5 


26 
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3 5.25 
1 11.33 


12 


4 


18 6 


2 9 


15 


2 6 


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8 2.33 
5 7. 5 


8 10.33 
6 3 


25 
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2 11.75 
1 8.33 


3 3 
1 11.33 


11.5 


5 


19 7 


2 10 


16 


2 4 


C72 
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8 7.25 
5 10.33 


9 3 
6 6 


26 
15 


3 1.25 
1 8.33 


3 5.25 
1 11.33 


11 


6 


20 8 


2 11 


17 


2 3 


C72 
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8 7.25 
5 10.33 


9 3 
•6 6 


25 
14 


2 11.75 
1 7 


3 3 
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10.5 


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21 9 


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C72 
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23 
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9.25 


10 


25 1 


3 4 


21 


1 11 


("78 
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9 3. 5 
5 10.33 


9 11. 5 

6 6 


24 
14 


2 10.33 

1 7 


3 1. 5 

1 10 


8.87 


11 


26 3 


3 6 


22 


I 10 


( 78 
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9 3. 5 
5 10.33 


9 11. 5 

6 6 


23 
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2 9 
1 7 


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1 10 


8.5 


12 


27 5 


3 8 


23 


1 9 


£78 


9 3. 5 


9 11. 5 


23 


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(54 


6 1 


6 8. 5 


14 


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1 10 




13 


28 7 


3 10 


24 


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C81 
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9 8 


10 4 


23 


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14 


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1 10 




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29 9 


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C81 
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7.75 


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6 3.75 


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14 


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1 10 




16 


32 1 


4 4 


27 


1 5 


("84 
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10 0.25 


10 8.25 


23 


2 9 


3 


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6 6.25 


7 1.75 


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1 10 




17 


33 3 


4 6 


28 


1 4 


("84 
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10 0.25 
6 3.75 


10 8.25 
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23 
13 


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3 

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6.66 


18 


34 6 


4 9 


29 


1 3 


("84 
(56 


10 0.25 


10 8.25 


22 


2 7. 5 


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TABLES, &C. 



TABLE II. — For Overshot Mills, with Stones 4 feet 6 inches diameter, to re- 
volve 99 times in a minute, pitch of the gears 4g and 4^ inches. 





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TABLES, &C. 



TABLE III. — Stones 5 feet diameter, to revolve 68 times in a minute, the pitch 
of the gears 4^ and 4^ inches. 



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TABLES. &C. 



303 



TABLE IV. — For Overshot Mills with Stones 5 feet 6 inches diameter, to re- 
volve 80 times in a minute, pitch of the gears 4| and 4^ inches. 



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304 OF CONSTRUCTING WHEELS. [CHAP. XXI. 

CHAPTER XXI. 

ARTICLE 129. 

DIRECTIONS FOR CONSTRUCTING UNDERSHOT WHEELS, SUCH AS SHOWN 
IN FIGURE 1, PLATE XIII. 

1. Dress the arms straight and square on all sides, and 
find the centre of each; divide each into 4 equal parts on 
the side, square, centre, scribe, and gauge them from the 
upper side across each point, on both sides, 6 inches each 
way from the centre. 

2. Set up a truckle or centre post, for a centre to frame 
the wheel on, in a level piece of ground, and set a stake 
to keep up each end of the arms level with the truckle, 
of convenient height to work on. 

3. Lay the first arm with its centre on the centre of 
the truckle, and take a square notch out of the upper side 
3-4ths of its depth, wide enough to receive the 2d arm. 

4. Make a square notch in the lower edge of the 2d 
arm, 1-4 of its depth, and lay it in the other, and they 
will joint, standing square across each other. 

5. Lay the 3d arm just equi-distant between the others, 
and scribe the lower arms by the side of the upper, and 
the lower edge of the upper by the sides of the lower 
arms. Then take the upper arm off and strike the square 
scribes, taking out the lower half of the 3d arm, and the 
upper half of the lower arms, and fit and lay them to- 
gether. 

6. Lay the 4th arm on the others, and scribe as di- 
rected before: then take 3-4ths of the lower edo-e of the 
4th arm, and 1-4 out of the upper edge of the others, and 
lay them together, and they will be locked together in 
the depth of one. 

7. Make a sweep-staff with a gimlet hole for the cen- 
tre at one end, which must be set by a gimlet in the 
centre of the arms. Measure from this hole half the dia- 
meter of the wheel, making a hole there, and another the 
depth of the shrouds towards the centre, making each 
edge of this sweep at the end next the shrouds, straight 



CHAP. XXI.] OF CONSTRUCTING WHEELS. 305 

towards the centre hole, to scribe the ends of the shrouds 
by. 

8. Circle both edges of the shrouds by the sweep, dress 
them to the proper width and thickness; lay out the laps 
5 inches long; set a gauge to a little more than one-third 
their thickness; gauge all their ends for the laps from 
the outsides ; cut them all out but the last, that it may 
be made a little longer, or shorter, as may suit to make 
the wheel the right diameter; sweep a circle on the arms 
to lay the shrouds to, while fitting them; put a small 
draw-pin in the middle of each lap, to draw the joints 
close; strike true circles both for the inside and outside 
of the shrouds, and If inch from the inside, where the 
arms are to be let in. 

9. Divide the circle into 8 equal parts, coming as near 
the middle of each shroud as possible ; strike a scribe 
across each to lay out the notch by, that is to be cut If 
inch deep, to let in the arm at the bottom, where it is to 
be forked to take in the remainder of the shroud. Strike 
a scribe on the arms with the same sweep that the stroke 
for the notches on the shrouds was struck with. 

10. Scribe square down on each side of the arms, at the 
bottom, where they are to be forked; make a gauge to fit 
the arms ; so wide as just to take in the shrouds*,' and 
leave If inch of wood outside of the mortise; bore 1 or 2 
holes through each end of the arms to draw-pin the 
shrouds to the arms when hung; mark all the arms and 
shrouds to their places, and take them apart. 

11. Fork the arms, put them together again, and put 
the shrouds into the arms ; draw-bore them, but not too 
much, which would be worse than too little; take the 
shrouds apart again, turn them the other side up, and 
draw the joints together with the pins, and lay out the 
notches for 4 floats between each arm, 32 in all, large 
enough for admitting keys to keep them fast, but allow- 
ing them to drive in when any thing gets under the 
wheel. The ends of the floats must be dove-tailed a lit- 
tle into the shrouds; when one side is framed, frame the 
other to fellow it. This done, the wheel is ready to 
hang, but remember to face the shrouds between the arms 

20 



306 OF CONSTRUCTING WHEELS. [CHAP. XXI. 

with inch boards, nailed on with strong nails, to keep the 
wheel firmly together. 



article 130. 

DIRECTIONS FOR DRESSING SHAFTS, &C. 

The shaft for a water wheel with 8 arms should be 16 
square, or 16 sided, about 2 feet diameter, the tree to 
make it being 2 feet 3 inches at the top end. When cut 
down, saw it off square at each end, and roll it on level 
skids, and if it be not straight, lay the rounding side down 
and view it, to find the spot for the centre at each end. 
Set the large compasses to half its diameter, and sweep 
a circle at each end, plumb a line across each centre, and 
at each side of the circle, striking chalk lines over the 
plumb lines at each side from end to end, and dress the 
sides plumb to these lines; turn it down on one side, set- 
ting it level ; plumb line, and dress off the sides to a 4 
square ; set it exactly on one corner, and plumb line, and 
dress off the corner to 8 square. In the same manner 
dress it to 16 square. 

To cut it square off to its exact length, stick a peg in 
the centre of each end, take a long square, (which may 
be made of boards,) lay it along the corner, the short end 
against the end of the peg, mark on the square where the 
shaft is to be cut, and mark the shaft by it at every cor- 
ner line, from mark to mark; then cut it off to the lines, 
and it will be truly square. 



article 131. 

TO LAY OUT THE MORTISES FOR THE ARMS. 

Find the centre of the shaft at each end, and strike a 
circle; plumb a line through the centre at each end to 
be in the middle of two of the sides ; make another scribe 
square across it; divide the distance equally between 
them, so as to divide the circle into 8 equal parts, and 



CHAP. XXI.] OF CONSTRUCTING WHEELS. 307 

strike a line from each of them, from end to end, in the 
middle of the sides; measure from the top end about 3 
feet, and mark for the arm of the water-wheel, and the 
width of the wheel, and make another mark. Take a 
straight-edged 10 feet pole, and put the end even with 
the end of the shaft, and mark on it even with the marks 
on the shaft, and by these marks measure for the arm at 
every corner, marking and lining all the way round. 
Then take the uppermost arms of each rim, and by them 
lay out the mortises, about half an inch longer than they 
are wide, which is to leave key room; set the compasses 
a little more than half the thickness of the arms, and set 
one foot in the centre line at the end of the mortise, 
striking a scribe each way to lay out the width by; this 
done, lay out 2 more on the opposite side, to complete 
the mortises through the shaft. Lay out 2 more, square 
across the first, one-quarter the width of the arm longer, 
inwards, towards the middle of the wheel. Take notice 
which way the locks of the arms wind, whether to right 
or left, and lay out the third mortises to suit, else it will 
be a chance whether they suit or not: these must be half 
the width of the arms longer, inwards. 

The 4th set of mortises must be three-fourths longer in- 
wards than the width of the arms; the mortises should be 
made rather hollowing than rounding, that the arms may 
slip in easily and stand fair. 

If there be 3 (which are called 6) arms to the cog- 
wheel, but one of them can be put through the sides of 
the shaft fairly; therefore, to lay out the mortises, divide 
the end of the shaft anew, into but 6 equal parts, by 
striking a circle on each end ; and without altering the 
compasses, step from one of the old lines, six steps round 
the circle, and from these points strike chalk lines, and 
they will be the middle of the mortises, which may be 
laid out as before, minding which way the arms lock, and 
making two of the mortises one-third longer than the 
width of the arm, extending one on one side, and the 
other on the other side of the middle arm. 

If there be but 2 (called 4) arms in the cog-wheel, 
(which will do where the number of cogs does not exceed 
60) they will pass fairly through the sides, whether the 



308 OF CONSTRUCTING WHEELS. [CHAP. XXI. 

shafts be 12 or 16 sided. One of these must be made 
one half longer than the width of the arms, to give room 
to put the arm in. 



article 132. 

TO PUT IN THE GUDGEONS. 

Strike a circle on the ends of the shaft to let on the 
end bands; make a circle all round, 2§ feet from each 
end, and saw a notch all round, half an inch deep. Lay 
out a square, round the centres, the size of the gudgeons, 
near the neck; lay the gudgeons straight on the shaft and 
scribe round them for their mortises; let them down with- 
in one-eighth of an inch of being in the centre. Dress 
off the ends to suit the bands; make 3 keys of good, sea- 
soned white oak, to fill each mortise above the gudgeons, 
to key them in, those next to the gudgeons to be 31 
inches deep at the inner end, and 1^ inch at their outer 
end, the wedge or driving key 3 inches at the head, and 
6 inches longer than the mortise, that it may be cut off, 
if it batter in driving; the piece next the band so wide 
as to raise half an inch above the shaft, when all are laid 
in. Then take out all the keys and put on the bands, 
and make 8 or 12 iron wedges about 4 inches long by 2 
wide, l-3d inch thick, at the end, not much tapered ex- 
cept half an inch at the small end, on one side next the 
wood; by means of a set, drive them in on each side the 
gudgeon extremely hard, at a proper distance apart. 
Then put in the keys again, and lay a piece of iron un- 
der each band, between it and the key, 6 inches long, 
half an inch thick in the middle, and tapering off at the 
ends; then/grease the keys well with tallow, and drive it 
well with a heavy sledge; after this, drive an iron wedge, 
half an inch from the two sides of each gudgeon, 5 inches 
long, about half an inch thick, and as wide as the gudgeon. 



CHAP. XXI,] OF CONSTRUCTING WHEELS. 309 



ARTICLE 133. 

OF COG-WHEELS. 

The great face cog-wheels require 3 (called 6) arms, if 
the number of cogs exceed 54 ; if less, 4 will do. We find 
by the table, example 43, that the cog-wheel must have 
69 cogs, with 4| inches pitch, the diameter of its pitch 
circle 8 feet 2 J inches, and of its outsides 8 feet 10 J inches. 
It requires 3 arms, 9 feet long; 14by3| inches; 12 cants, 
6£ feet long, 16 by 4 inches. (See it represented, fig. 1, 
Plate XVII.) 

To frame it, dress and lock the arms together, (fig. 6, 
PI. XVII.) as directed, Art. 129, only mind to leave one- 
third of each arm uncut, and to lock them the right way 
to suit the winding of the mortises in the shaft, which is 
best found by putting a strip of board in the middle mor- 
tise, and supposing it to be the arm, mark which way it 
should be cut, then apply the board to the arm, and mark 
it. The arms being laid on a truckle, as directed, Art. 
1 29, make a sweep, the sides directing to the centre, 2 
feet from the outer end to scribe by; measure on the 
sweep, half the diameter of the wheel ; and by it circle out 
the back edges of the cants, all of one width in the middle; 
dress them, keeping the best faces for , the face side of 
the wheel; make a circle on the arms half an inch larger 
than the diameter of the wheel, laying 3 of the cants 
with their ends on the arms, at this circle, at equal dis- 
tances apart. Lay the other three on the top of them 
so as to lap equally; scribe them both under and top, and 
gauge all for the laps from the face side; dress them out 
and lay them together, and joint them close; draw-pin 
them by an inch pin near their inside corners: this makes 
one-half of the wheel, shown fig. 5. Raise the centre 
level with that half; strike a circle near the outside, and 
find the centre of one of the cants ; then, with the sweep 
that described the circle, step on the circle 6 steps, be- 
ginning at the middle of the cant, and these steps will 
show the middle of all the cants, or places for the arms. 
Make a scribe from the centre across each ; strike another 
circle exactly at the corners, to place the corners of the 



310 OF CONSTRUCTING WHEELS. [CHAP. XXI. 

next half by, and another about 2| inches farther out than 
the inside of the widest part of the cant, to let the arms 
in by; lay on three of the upper cants, the widest part 
over the narrowest part of the lower half, the inside to 
be at the point where the corner circle crosses the cen- 
tre lines. Saw off the ends, at the centre scribes, and fit 
them down to their places, doing the same with the rest. 
Lay them all on, and joint their ends together: draw-pin 
them to the lower half, by inch pins, 2 inches from then- 
inner edges, and 9 inches from their ends. Raise the 
centre level with the wheel; plane a little off the rough 
off the face, and strike the pitch circle, and another 4 
inches inside, for the width of the face; strike another 
very near it, in which drive a chisel, half an inch deep, 
all round, and strike lines, with chalk, in the middle^of 
the edge of the upper cants, and cut out of the solid, half 
of the upper cants, which raises the face; divide the 
pitch circle into 69 equal parts, 4§ inches pitch, begin- 
ning and ending in a joint; strike two other circles each 
21 inches from the pitch circle, and strike central scribes 
between the cogs, and where they cross the circles put 
in pins, as many as there are cogs, half on each circle; 
find the lowest part on the face, and make the centre le- 
vel with it; look across in another place, square with the 
first, and make it level with the centre also; then make the 
face straight, from these four places, and it will be true. 
Strike the pitch circle, and divide it over again, and 
strike one circle on each side of it, 1 inch distance, for 
the cog mortises; sweep the outside of the wheel and in- 
side of the face, and two circles |ths of an inch from them 
to dress off the corners; strike a circle of two inches dia- 
meter on the centre of each cog, and with the sweep 
strike central scribes at each side of these circles for the 
cog mortises; bore and mortise half through; turn the 
wheel, dress and mortise the back side, leaving the arms 
from under it ; strike a circle on the face edge of the 
arms, equal in diameter to that struck on the face of the 
half wheel, to let them in by; saw in square, and take out 
41 inches, and let them into the back of the wheel 11 
inch deep, and bore a hole 1| inch into each arm, to pin 
it to the wheel. 



CHAP. XXI.] OF SILLS, SPUR-BLOCKS, &C. 311 

Strike a circle°on the arms one inch less than the dia- 
meter of the shaft, make a key 8 inches long, 1^ thick, 
3i at the butt, and 2| inches at the top end, and by it lay 
out the mortises, two on each side of the shaft, in each 
arm to hang the wheel by. 



article 134. 

OF SILLS, SPUR-BLOCKS AND HEAD-BLOCKS. 

See a side view of them in Plates XIII., XIV., XV., 
and XVI., and a top view of them, with their keys, at the 
end of the shaft, Plate XVIII. The sills are generally 
12 inches square. Lay them on the wall as firmly as 
possible, and one 3 feet farther out; on these lay the spurs, 
which are 5 feet long, 7 by 7 inches, 3 feet apart, notched 
and pinned to the sills: on these are set the head-blocks, 
14 by 12 inches, 5 feet long, let down with a dove-tail 
shoulder between the spurs, to support keys to move it 
end-wise, and let two inches into the spurs with room for 
keys, to move it sidewise, and hold it to its place ; see fig. 
33 and 34, Plate XVIII. The ends of the shaft are let 
2 inches into the head-blocks, to throw the weight more 
on the centre. 

Provide two stones, 5 or 6 inches square, very hard 
and clear of grit, for the gudgeons to run on, let them 
into the head blocks, put the cog-wheel into its place, 
and then put in the shaft on the head-blocks, in its place. 

Put in the cog-wheel arm, lock them together, and pin 
the wheel to them; then hang the wheel, first by the 
keys to make it truly round, and then by side wedges, to 
make it true in face; turn the wheel, and make two cir- 
cles, one on each side of the cog-mortises, half an inch 
from them, so that the head of the cogs may stand be- 
tween them equally. 



312 OF COGS. [chap. XXI. 



ARTICLE 135. 

OF COGS J THE BEST TIME FOR CUTTING, AND MANNER OF SEASONING 

THEM. 

Cogs should be cut 14 inches long, and 3^ inches square, 
this should be done when the sap runs at its fullest, at 
least a year before they are used, that they may dry with- 
out cracking. If either hickory or white oak be cut when 
the bark is set, they will worm-eat, and if dried hastily, 
will crack; to prevent which, boil them and dry them 
slowly, or soak them in water, a year, (20 years in mud 
and fresh water would not hurt them :) when they are 
taken out, they should be put in a hay-mow, under the 
hay, where, while foddered away, they will dry without 
cracking; but this often takes too long a time. I have 
discovered the following method of drying them in a few 
days, without cracking. I have a malt kiln with a floor 
of laths two inches apart; I shank the cogs, hang them, 
shank downwards, between the laths, cover them with a 
hair cloth, make a wood fire, and the smoke prevents 
them from cracking. Some dry them in an oven, which 
ruins them. Boards, planks, or scantling, are best dried 
in a kiln, covered so as to keep the smoke amongst them. 
Instead of a malt kiln, dig a cave in the side of a hill, 6 
feet deep, 5 or 6 feet wide, with a post in each corner 
with plates on them, on which lay laths on edge, and pile 
the cogs on end, nearly perpendicular, so that the smoke 
can pass freely through, or amongst them. Cover them 
slightly with boards and earth, make a slow fire, and 
close up the sides, and renew the fire once a day, for 12 
or 15 days; they will then dry without cracking. 



ARTICLE 136. ' 
OF SHANKING, PUTTING IN, AND DRESSING OFF COGS. 

Straighten one of the heart sides for the shank, make 
a pattern, the head 4, and shank 10 inches long, and 2 
inches wide at the head, 1| at the point; lay it on the 
cog, scribe the shank and shoulders, for the head, saw in 



CHAP. XXI.] OF COGS. 313 

and dress offthe sides; make another pattern of the shank, 
without the head, to scribe the sides and dress off the 
backs by, laying it even with the face, which is to have 
no shoulder; take care, in dressing them off, that the axe 
do not strike the shoulder; if it do, it will crack there in 
drying, (if they be green;) fit and drive them in the mor- 
tises exceedingly tight, with their shoulders foremost, 
when at work. When the cogs are all in, fix two pieces 
of scantling, for rests, to scribe the cogs by, one across 
the cog-pit, near the cogs, another in front of them ; fix 
them firmly. Hold a pointed tool on the rest, and scribe 
for the length of the cogs, by turning the wheel, and saw 
them off 3| inches long; then move the rest close to them, 
and fix it firmly; find the pitch circle on the end of the 
cogs, and, by turning the wheel, describe it there. 

Describe another line |th of an inch outside thereof, 
to set the compasses in to describe the face of the cogs by, 
and another at each side of the cogs to dress them to their 
width : then pitch the cogs by dividing them equally, so 
that, in stepping round, the compasses may end in the 
point where they began; describe a circle, in some par- 
ticular place, with the pitch, that it may not be lost: 
these points must be as nearly as possible of a proper dis- 
tance for the centre from the back of the cogs: find the 
cog to the back of which this point comes nearest, and 
set the compasses from that point to the back of the cog; 
with this distance set off the backs of all the cogs equally, 
on the circle, £th of an inch outside of the pitch circle, 
and from these points, last made, set offthe thickness of 
the cogs, which should, in this case, be 1 j inch. 

Then describe the face and back of the cogs by setting 
the compasses in the hindmost point of one cog, and sweep- 
ing over the foremost point of another, for the face, and 
in the foremost point of one, sweeping over the hindmost 
of the other, for the back part ; dress them off on all sides, 
tapering about |th of an inch, in an inch distance; try 
them by a gauge, to make them all alike; take a little off 
the corners, and they are finished. 



314 OF WALLOWERS AND TRUNDLES. [CHAP. XXI. 

ARTICLE 137. 

OF THE LITTLE COG-WHEEL AND SHAFT. 

The process of making this is similar to that of the big 
cog-wheel. Its dimensions we find by the table, and the 
same example, (43,) to be 52 cogs, 4-i pitch; diameter of 
pitch circle 5 feet 10 J inches, and from out to out, 6 feet 
6 inches. 

It requires 2 arms, 6 feet 6 inches long, 11 by 3^ 
inches; 8 cants, 5 feet 6 inches, 17 by 3| inches. (See 
it, fig. 4, Plate XVII.) 

Of the Shaft. 

Dress it 8 feet long, 14 by 14 inches square, and de- 
scribe a circle on each end 14 inches diameter; strike two 
lines through the centre, parallel to the sides, and divide 
the quarters into 4 equal parts, each ; strike lines across 
the centre at each part at the end of these lines; strike 
chalk lines from end to end, to hew off the corners by, and 
it will be 8 square ; lay out the mortises for the arms, put on 
the bands, and put in the gudgeons, as with the big shaft. 



ARTICLE 138. 

DIRECTIONS FOR MAKING WALLOWERS AND TRUNDLES. 

By example 43, in the table, the wallower is to have 
26 rounds 4| pitch: the diameter of its pitch circle is 3 
feet 1\ inch, and 3 feet 4^ inches from outside: (see fig. 
3, Plate XVII.) Its head should be 3| inches thick, dow- 
eled truly together, or made with double plank, crossing 
each other. Make the bands 3 inches wide, \\h of an inch 
thick, evenly drawn ; the heads must be made to suit the 
bands, by setting the compasses so that they will step 
round the inside of the band in 6 steps; with this distance 
sweep the head, allowing about J^-th of an inch outside, 
in dressing, to make such a large band tight. Make them 
hot alike all round with a chip fire, which swells the 
iron ; put them on the head while hot, and cool them with 
water, to keep them from burning the wood too much, 



CHAP. XXI.] OF HANGING WHEELS. 315 

but not too fast, lest they snap: the same mode serves for 
hooping all kinds of heads. 

Dress the head fair after banding, and strike the pitch 
circle and divide it by the same pitch with the cogs; 
bore the holes for the rounds with an auger of at least If 
inch ; make the rounds of the best wood, 2| inches dia- 
meter, and 11 inches between the shoulders, the tenons 
4 inches, to fit the holes loosely, until within 1 inch of 
the shoulder, then drive it tight. Make the mortises 
for the shaft in the heads, with notches for the keys to 
hang it by. When the rounds are all driven into the 
shoulders, observe whether they stand straight ; if not, 
they may be set fair by putting the wedges nearest to one 
side of the tenon, so that the strongest part may incline to 
draw them straight: this should be done with both heads. 



ARTICLE 139. 

OF FIXING THE HEAD-BLOCKS AND HANGING THE WHEELS. 

The head-blocks, for the wallower shaft, are shown in 
Plate XVIII. Number 19 is one called a spur, 6 feet 
long and 15 inches deep, one end of which, at 19, is let 
1 inch into the top of the husk-sill, which sill is 1^ inch 
above the floor, the other end tenoned strongly into a 
strong post, 14 by 14 inches, 12 or 14 feet long, standing 
near the cog-wheel, on a sill in the bottom of the cog-pit ; 
the top is tenoned into the husk-plank; these are called 
the tomkin posts. The other head-blocks appear at 20 
and 28. In these large head-blocks there are small ones 
let in that are 2 feet long, and 6 inches square, with a 
stone in each for the gudgeons to run on. That one in 
the spur 19 is made to slide, to put the wallower in and 
out of gear, by a lever screwed to its side. 

Lay the centre of the little shaft level with the big 
one, so as to put the wallower to gear § the thickness of 
the rounds deep, into the cog-wheel; put the shaft into 
its place, hang the wallower, and gauge the rounds to 
equal distance where the cogs take. Hang the cog-wheel, 



316 OF SINKING THE BALANCE-RYNE. [CHAP. XXI. 

put in the cogs, make the trundle as directed for the 
wallower. (See fig. 4, Plate XVII.) 



ARTICLE 140. 

DIRECTIONS FOR PUTTING IN THE BALANCE-RYNE. 

Lay it in the eye of the stone, and fix it truly in the 
centre; to do which, make a sweep by putting a long pin 
through the end, to reach into, and fit, the pivot hole in 
the balance-ryne ; by repeated trials on the opposite side, 
fix it in the centre ; then make a particular mark on the 
sweep, and others to suit it on the stone, scribe round the 
horns, and with picks and chisels sink the mortises to 
their proper depth, trying, by the particular marks made 
for the purpose, by the sweep, if it be in the centre. Put 
in the spindle with the foot upwards, and the driver on 
its place, while one holds it plumb. Set the driver over 
two of the horns, if it has four, but between them if it 
has but two. When the neck is exactly in the centre of 
the stone, scribe round the horns of the driver, and let 
it into the stone, nearly to the balance, if it has four horns. 
Put the top of the spindle in the pivot-hole, to try whe- 
ther the mortises let it down freely on both sides. 

Make a tram, to set the spindle square by, as follows : 
take a piece of board, cut a notch in one side, atone end, 
and hang it on the top of the spindle, by a little peg in 
the shoulder of the notch, to go into the hole in the foot, 
to keep it on: let the other end reach down to the edge 
of the stone; take another piece, circle out one end to fit 
the spindle neck, and make the other end fast to the low- 
er end of the hanging piece near the stone, so as to play 
round level with the face of the stone, resting on the 
centre-hole in the foot, and against the neck ; put a bit of 
quill through the end of the level piece, that will touch 
the edge of the stone as it plays round. Make little 
wedges, and drive them in behind the horns of the driver, 
to keep both ends, at once, close to the sides of the mor- 
tises they bear against when at work, keeping the pivot 
or cock-head in its hole in the balance; try the tram gen- 



CHAP. XXI.] OF THE CRANE AND LIGHTER STAFF. 317 

tly round, and mark where the quill touches the stone 
first, and dress off the bearing sides of the mortises for the 
driver,, until it will touch equally all round, giving the 
driver^liberty to move endwise, and sidewise, so that the 
stone may rock an inch either way. The ryne and driver 
must be sunk |ths of an inch below the face of the stone. 
Then hang the trundle firmly and truly on the spindle; 
put it in its place, to gear in the little cog-wheel. 



article 141. 

TO BRIDGE THE SPINDLE. 

Make a little tram of a piece of lath, 3 inches wide at 
one end, and one inch at the other, make a mortise in the 
wide end, and put it on the cock-head, and a piece of 
quill in the small end, to play round the face of the stone; 
then, while one turns the trundle, another observes where 
the quill touches first, and alters the keys of the bridge- 
tree, driving the spindle-foot toward the part the quill 
touches, until it does so equally all round. Case the stone 
neatly round, within 2 inches of the face. 



article 142. 

OF THE CRANE AND LIGHTER STAFF. 

Make a crane, with a screw and bale, for faking up 
and putting down the stone. (See it represented in 
Plate XL, fig. 2 and 3.) Set the post out of the way as 
much as possible, let it be 9 by 6 inches in the middle, 
the arm 9 by 6, the brace 6 by 4; make a hole plumb 
over the spindle, for the screw ; put an iron washer on 
the arm under the female screw, nail it fast; the length of 
the screw in the worm part should exceed half the dia- 
meter of the stone, and it should reach 10 inches below it; 
the bale must touch only at the ends to give the stone li- 
berty to turn, the pins to be 7 inches long, l-l thick, the 
bale to be 2£ inches wide in the middle, and If inch 
wide at the end; the whole should be made of the best 



318 OF MAKING A HOOP FOR THE MILL-STONE. [cHAP. XXI. 

iron ; for if either of them break, the danger would be 
great: the holes in the stones should be nearest to the up- 
per side of it. Raise the runner by the crane, screw, 
and bale, turn it and lay it down, with the horns of the 
driving ryne in their right places, as marked, it being 
down, as it appears in Plate XXI., fig. 9. Make the 
lighter staff C C, to raise and lower the stone in grinding, 
about 6 feet long, 3* by 21 inches at the large end, and 
2 inches square at the small end, with a knob on the up- 
per side. Make a mortise through the but-end, for the 
bray-iron to pass through, which goes into a mortise 4 
inches deep in the end of the bray at b, and is fastened 
with a pin; it may be 2 inches wide and half an inch 
thick, made plain, with 1 hole at the lower, and 5 or 6 
at the upper end ; it should be set in a staggering posi- 
tion. This lighter is fixed in front of the mill-beam, at 
such a height as to be handy to raise and lower at plea- 
sure ; a weight of 4 lbs. is hung to the end of it by a strap, 
which laps two or three times round, and the other end 
is fastened to the post below, that keeps it in its place. 
Play the lighter up and down, and observe whether the 
stone rises and falls flat on the bed-stone; if it do, draw a 
little water, and let the stone move gently round; then 
see that all things be right, and draw a little more wa- 
ter, let the stone run at a moderate rate, and grind the 
faces a few minutes. 



article 143. 

DIRECTIONS FOR MAKING A HOOP FOR THE MILL-STONE. 

Take a white pine or poplar board, 8 inches longer 
than will go round the stone, and 2 inches wider than the 
top of the stone is high, dress it smooth, and gauge it 
one inch thick, run a gauge mark |th of an inch from the 
outside, divide the length into 52 parts, and saw as many 
saw-gates square across the inside to the gauge-line. 
Take a board of equal width, 1 foot long, nail one-half 
of it on the outside at one end of the hoop, lay it in wa- 
ter a day or two to soak, or frequently sprinkle the out- 



CHAP. XXI.] OF FACING STONES, &C. 319 

side with hot water, during an hour or two. Bend it 
round so that the ends meet, and nail the other end to 
the short board, put sticks across inside, in various direc- 
tions, to press out the parts that bend least, and make it 
truly round. Make a cover for the hoop, (such as is re- 
presented in Plate XIX., fig. 23;) 8 square inside, and 1 
inch outside the hoop. It consists of 8 pieces lapped 
one over another, the black lines showing the joints as 
they appear when made, the dotted lines the under parts 
of the laps. Describe it on the floor, and make a pattern 
to make all the rest by ; dress all the laps, fit and nail them 
together by the circle on the floor, and then nail it on 
the hoop; put the hoop over the stone, and scribe it to fit 
the floor. 



article 144. 

OF GRINDING SAND TO FACE THE STONES. 

Lay boards over the hoop to keep the dust from flying, 
and take a bushel or two of dry, clean, sharp sand, teem it 
gently into the eye, while the stone moves at a moderate 
rate, continuing to grind for an hour or two: then take 
up the stones, sweep them clean, and pick the smoothest, 
hardest places, and lay the stone down again, and grind 
more sand as before, turning off the back, (if it be a burr,) 
taking great care that the chisel do not catch ; take up 
the stone again, and make a red staff, equal, in length, 
to the diameter of the stone, and 3 by 2\ inches; paint 
it with red paint and water, and rub it over the face of 
the stone in all directions, the red will be left on the 
highest and hardest parts, which must be picked down, 
making the bed-stone perfectly plain, and the runner a 
little concave, about £th of an inch at the eye, and les- 
sening gradually at about 8 inches from the skirt. If 
they be close, and have much face, they need not touch, 
or flour, so far as if they be open, and have but little 
face; those things are necessarily left to the judgment of 
the mill-wright and miller. 



320 OF FURROWING STONES. [CHAP. XXI. 

ARTICLE 145. 
DIRECTIONS FOR LAYING OUT THE FURROWS IN THE STONES, &C. 

If they be five feet in diameter, divide the skirt into 
16 equal parts, called quarters; if feet, into 18; if 7 
feet, into 20 quarters. Make two strips of board, one an 
inch, and the other 2 inches wide; stand with your face 
to the eye, and if the stone turn to the right when at 
work, lay the strip at one of the quarter divisions; and 
the other at the left hand side, close to the eye, and mark 
with a flat-pointed spike for t a master furrow: they are 
all to be laid out the same way in both stones, for when 
their faces are together, the furrows should cross each 
other like shears in the best position for cutting cloth. 
Then, having not fewer than 6 good picks, proceed to 
pick out all the master furrows, making the edge next 
the skirt and the end next the eye, the deepest, and the 
feather edge not half so deep as the back. 

When all the master furrows are picked out, lay the 
broad strip next to the feather edges of all the furrows, 
and mark the head lands of the short furrows, then lay 
the same strip next the back edges, and mark for the 
lands, and lay the narrow strip, and mark for the furrows, 
and so mark out the lands and furrows, minding not 
to cross the head lands, but leaving it between the master 
furrows and the short ones of each quarter. But if they 
be close country stones, lay out both furrows and lands 
with the narrow strip. 

The neck of the spindle must not be wedged too tight, 
else it will burn loose; bridge the spindle again; put a 
collar round the spindle neck, but under it put a piece 
of an old stocking, with tallow rolled up in it, about a 
finger thick ; tack it closely round the neck ; put a piece 
of stiff leather about 6 inches diameter on the cock-head 
under the driver, to turn with the spindle and drive off 
the grain, &c, from the neck; grease the neck with tal- 
low every time the stone is up. 

Lay the stone down and turn off the back smooth, and 



CHAP. XXI.] OF THE HOPPER, SHOE, AND FEEDER. 321 

grind more sand. Stop the mill, raise the stone a little, 
and balance it truly with a weight laid on the lightest 
side. Take lead equal to its weight, melt it, and run 
it into a hole made in the same place in the plaster; this 
hole should be largest at bottom, to keep it in ; fill the 
hole with the plaster, take up the runner again, try the 
staff over the stones, and if in good face, give them a nice 
dressing, and lay them down to grind wheat. 



article 146. 

DIRECTIONS FOR MAKING A HOPPER, SHOE, AND FEEDER. 

The dimensions of the hopper of a common mill is 4 
feet at the top, and 2 feet deep, the hole in the bottom 3 
inches square, with a sliding gate in the bottom of the 
front to lessen it at pleasure: the shoe 10 inches long, 
and 5 wide in the bottom, of good sound oak. The side 
7 or 8 inches deep at the hinder end, 3 inches at the 
foremost end, 6 longer than the bottom of the fore end, 
slanting more than the hopper behind, so that it may 
have liberty to hang down 3 or 4 inches at the fore end, 
which is hung by a strap called the feeding string, pass- 
ing over the fore end of the hopper-frame, and lapping 
round a pin in front of the meal-beam, which pin will 
turn by the hand, and which is called the feeding-screw. 

The feeder is a piece of wood turned in a lathe, about 
20 inches long, 3 inches diameter in the middle, against 
the shoe, tapered off to 1 § inch at the top ; the lower 
end is banded, and a forked iron driven in it, that spans 
over the ryne, fitting into notches made on each side, to 
receive it, directly above the spindle, with which it turns, 
the upper end running in a hole in a piece across the 
hopper-frame. In the large part, next the shoe, 6 iron 
knockers are set, 7 inches long, half an inch diameter, 
with a tang at each end, turned square to drive into the 
wood, these knock against and shake the shoe, and there- 
by shake in the grain regularly. 

You may now put the grain into the hopper, draw wa- 
21 



322 OF BOLTING CHESTS AND REELS. [CHAP. XXI. 

ter on the mill, and regulate the feed by turning the feed 
screw, until the stream falling into the eye of the stone, 
be proportioned to the size thereof, or the power of the 
mill. Here ends the mill-wright's work, with respect to 
grinding, and the miller takes the charge thereof. 



article 147. 

OF BOLTING CHESTS AND REELS. 

Bolting chests and reels are of different lengths, ac- 
cording to the use for whjch they are intended. Com- 
mon country chests (a top view of one of which is shown 
in Plate XIX., fig. 9,) are usually about 10 feet long, 3 
feet wide, and 7 feet 4 inches high, with a post in each 
corner ; the bottom 2 feet from the floor, with a board 
18 inches wide, set slanting in the back side, to cast the 
meal forward in the chest, that it may be easily taken up; 
the door is of the whole length of the chest, and two 
feet wide, the bottom board below the door sixteen inches 
wide. 

The shaft of the reel is equal in length with the chest, 
4 inches diameter, 6 square, two bands on each end, 3^ 
and 3| inches diameter: gudgeons 13 inches long, i of 
an inch diameter, 8 inches in the shaft, rounded at the 
neck 2~ inches, with a tenon for a socket, or handle, 
there are six ribs If inch deep, 1| inch thick, \ an 
inch at the tail, and If inch at the head, shorter than 
the shaft, to leave room for the meal to be scouted in at 
the head, and the bran to fall out at the tail; there are 
four sets of arms, that is 12 of them, If inch wide, and 
4 thick. The diameter of the reel from out to out of 
the ribs, is one third part of the double width of the 
cloth. A round wheel, made of inch boards, in diame- 
ter equal to the outside of the ribs, and 4| inches wide, 
measuring from the outside towards the centre, (which is 
taken out,) is to be framed to the head of the reel, to 
keep the meal from falling out at the head, unbolted. 
Put a hoop 4| inches wide, and | thick, round the tail 



CHAP, XXI.] OF SETTING BOLTS TO GO BY WATER. 323 

to fasten the cloth to. The cloth is sewed, two widths 
of it together, to reach round the reel, putting a strip of 
strong linen, 7 inches wide at the head, and 5 inches at 
the tail of the cloth, by which to fasten it to the reel. 
Paste on each rib a strip of linen, soft paper, or chamois 
leather, (which is the best) ] | inch wide, to keep the 
cloth from fretting. Then put the cloth on the reel 
tight, sew or nail it to the tail, and stretch it length- 
wise as hard as it will bear, nailing it to the head. — Six 
yards of cloth cover a ten feet reel. 

Bolting reels for merchant mills are generally longer 
than for country work, and every part should be stronger 
in proportion. They are best when made to suit the 
wide cloths. The socket gudgeons at the head should 
be much stronger, they being apt to wear out, and trou- 
blesome to repair. 

The bolting-hopper is made to pass through the floor 
above the chest, is 12 inches square at the upper, and 10 
inches at the lower end; the foremost side 5 inches, and 
the back side 7 inches from the top of the chest. 

The shoe 2 feet long at the bottom of the side pieces, 
slanting to suit the hopper at the hinder end, set 4 inches 
higher at the hinder than the fore end, the bottom 17 
inches long, and 10 inches wide. There should be a bow 
of iron riveted to the fore end, to rest on the top of the 
knocking wheel, which is fixed on the socket gudgeons at 
the head of the chest, and is 10 inches diameter, 2 inches 
thick, with 6 half rounds, cut out of its circumference, 
forming knockers to strike against the bow, and lift the 
shoe | of an inch every stroke, to shake in the meal. 



ARTICLE 148, 
OF SETTING BOLTS TO GO BY WATER. 

The bolting reels are set to go by water as follows:— 
Make a bridge 6 by 4 inches, and 4 inches longer than 
the distance of the tomkin posts, described Art. 139 ; set 
it between them, on rests fastened into them 10 inches 
below the cogs of the cog-wheel, and the centre of it half 
the diameter of the spur-wheel in front of them; on this 



324 OF MAKING BOLTING WHEELS. [CHAP. XXI. 

bridge is set the step gudgeon of an upright shaft, with 
a spur-wheel of 16 or 18 cogs to gear into the cog-wheel. 
Fix a head-block to the joists of the 3d floor for the up- 
per end of this shaft; put the wheel 28, (PI. XIX.) on it; 
hang another head-block to the joists of the 2d floor, near 
the corner of the mill at 6, for the step of the short up- 
right shaft that is to be fixed there, to turn the reels 1 
and 9. Hang another head-block to the joists of the 3d 
floor, for the upper end of the said short upright, and fix 
also head-blocks for the short shaft at the head of the 
reels, so that the centres of all these shafts will meet. 
Then fix a hanging post in the corner 5, for the gudgeon 
of the long horizontal shaft 27 — 5 to run in. After the 
head-blocks are all fixed, then measure the length of each 
shaft, and make them as follows : namely : — 

The upright shaft 5£ inches for common mills, but if 
for merchant-work, with Evans' elevators, &c, added, 
make it larger, say 6 or 7 inches; the horizontal shaft 27 
— 5, and all the others 5 inches diameter. Put a socket- 
gudgeon in the middle of the long shafts, to keep them 
steady; make them 8, or 16, square, except at the end 
where the wheels are hung, where they must be 4 square. 
Band their ends, put in the gudgeons, and put them in 
their proper places in the head-blocks, to mark where 
the wheels are to be put on them. 



article 149. 

OF MAKING BOLTING WHEELS. 

Make the spur wheel for the first upright, with a A\ 
inch plank; the pitch of the cogs, the same as the cog- 
wheel, into which it is to work; put two bands | of an 
inch wide, one on each side of the cogs, and a rivet be- 
tween each cog, to keep the wheel from splitting. 

To proportion the cogs in the wheels, to give the bolts 
the right motion, the common way is — 

Hang the spur-wheel, and set the stones to grind with 
a proper motion, and count the revolutions of the upright 
shaft in a minute; compare its revolutions with the revo- 



CHAP. XXI.] OF MAKING BOLTING-WHEELS. 325 

lutions that a bolt should have, which is about 36 revo- 
lutions in a minute. If the upright go | more, put | less 
in the first driving wheel than in the leader; suppose 15 
in the driver, then 18 in the leader: but if their difference 
be more, (say one-half,) there must be a difference in the 
next two wheels; observing that if the motion of the up- 
right shaft be greater than that of the bolt should be, the 
driving wheel must be proportionably less than the leader : 
but if it be slower, then the driver must be greater in pro- 
portion. The common size of bolting wheels is from 14 
to 20 cogs; if less than 14, the head-blocks will be too 
near the shafts. 

Common bolting wheels should be made of plank, at 
least 3 inches thick, well seasoned; and they are best 
when as wide as the diameter of the wheel, and banded 
with bands nearly as wide as the thickness of the wheel, 
the bands may be made of rolled iron, about | of an inch 
thick. Some make the wheels of 2 inch plank, crossed, 
and no bands ; but this proves no saving, as they are apt 
to go to pieces in a few years. (For hooping wheels, see 
Art. 136, and for finding the diameter of the pitch cir- 
cle, see Art. 126.) The wheels, if banded, are gene- 
rally two inches more in diameter than the pitch circle; 
but if not, they should be larger. The pitch or distances 
of the cogs are different; if to turn 1 or 2 bolts, 2\ inches, 
but, if more, 2|; if they are to do much heavy work, 
they should not be less than 3 inches. Their cogs, in 
thickness, are half the pitch : the shank must drive tight- 
ly in an inch auger hole. 

When the mortises are made for the shafts in the head, 
and notches for the keys to hang them, drive the cogs in 
and pin their shanks at the back side, and cut them off 
half an inch from the wheel. 

Hang the wheels on the shafts so that they will gear a 
proper depth, about § the thickness of the cogs; dress all 
the cogs to equal distances by a gauge; then put the 
shafts in their places, the wheels gearing properly, and 
the head-blocks all secure; set them in motion by water. 
Bolting reels should turn so as to drop the meal on the 
back side of the chest, as it will then hold more, and will 
not cast out the meal when the door is opened. 



326 OF ROLLING-SCREENS. [CHAP. XXI. 



ARTICLE 150. 

OF ROLLING-SCREENS. 

These are circular sieves, moved by water, and are 
particularly useful in cleaning wheat for merchant-work. 
They are of different constructions. 

1st. Those of one coat of wire with a screw in them. 

2dly. Those of two coats, the inner one nailed to six 
ribs, the outer one having a screw between it and the 
inner one. 

3dly. Those of a single coat, and no screw. 

The first kind answers well in some, but not in all 
cases, because they must turn a certain number of times 
before the wheat can get out, and the grain has not so 
good an opportunity of separating; there being nothing 
to change its position, it floats a considerable distance 
with the same grains uppermost. 

The double kinds are better, because they may be 
shorter, and take up less room, but they are more diffi- 
cult to keep clean. 

The 3d kind has this advantage; we can keep the grain 
in them a longer or shorter time, at pleasure, by raising 
or lowering the tail end, and it is also tossed about more; 
but they must be longer. They are generally 9 or 10 feet 
long, 2 feet 4 inches diameter, if to clean for two or three 
pairs of stones; but if for more, they should be larger ac- 
cordingly: they will clean for from one to six pairs of 
stones. They are made 6 square, with 6 ribs, which lie 
flatwise, the outer corners taken off to leave the edges \ 
of an inch thick; the inner corners are brought nearly to 
sharp edges; the wire work is nailed on with 14 ounce 
tacks. 

The screens are generally moved by the same upright 
shaft that moves the bolts, which has a wheel on its up- 
per end, with two sets of cogs: those that strike down- 
wards, gear into a wheel striking upwards, which turns 
a laying shaft, having two pulleys on the other end, one 
of 24 inches diameter, to turn a fan with a quick motion, 
the other of 8 inches, which conducts a strap to a pulley, 



CHAP. XXI.] OF FANS, &C. 327 

24 inches diameter, on the gudgeon of the rolling screen, 
to reduce its motion, to about 15 revolutions in a minute. 
(See fig. 19, Plate XIX.) This strap gearing may do for 
mills in a small way, but where they are in perfection 
for merchant-work, with elevators, &c, and have to clean 
wheat for 2, 3, or 4 pairs of stones, they should be moved 
by cogs. 



ARTICLE 151. 

OF FANS. 

The Dutch fan is a machine of great use for blowing 
the dust and other light stuff from among the wheat ; 
there are various sorts of them; those that are only for 
blowing the wheat as it falls from the rolling-screen, are 
generally about 15 inches long, and 14 inches wide, in 
the wings, and have no riddle or screen in them. 

To give motion to a fan of this kind, put a pulley 7 
inches diameter, on its axle, to receive a band from a 
pulley on the shaft that moves the screen, which pulley 
may be of 24 inches diameter, to give a swift motion; 
when the band is slack it slips a little on the small pul- 
ley, and the motion is retarded, but when tight the mo- 
tion is quicker ; by this the blast is regulated. 

Some use Dutch fans complete, with riddle and screen 
under the rolling screen, for merchant-work; and again 
use the fan alone for country-work. 

The wings of those which are the common farmers' 
wind-mills, or fans, are 18 inches long, and 20 inches 
wide ; but in mills they are set in motion with a pulley 
instead of a cog-wheel and wallower. 



article 152. 

OF THE SHAKING SIEVE. 

Shaking sieves are of considerable use in country mills, 
to sift Indian meal, separating it, if required, into seve- 



328 OF THE SHAKING SIEVE. [CHAP. XXI. 

ral degrees of fineness; and to take the hulls out of buck- 
wheat meal, which are apt to cut the bolting cloth; also 
to take the dust out of the grain, if rubbed before ground : 
they are sometimes used to clean wheat, or screenings, 
instead of rolling screens. 

If they are for sifting meal, they are 3 feet 6 inches 
long, 9 inches wide, 3| inches deep; (see it, fig. 16, Plate 
XVIII.) The wire-work is 3 feet long and 8 inches 
wide : across the bottom of the tail end is a board 6 inches 
wide to the top of which the wire is tacked, and then 
this board and wire are tacked to the bottom of the frame, 
leaving an opening at the tail end for the bran to fall into 
the box 17, the meal falling into the meal-trough 15; the 
head piece should be strong, to hold the iron bow at 15, 
through which the lever pa'sses that shakes the sieve, 
which is effected in the following manner. Take two 
pieces of hard wood, 15 inches long, and as wide as the 
spindle, and so thick that when one is put on each side 
just above the trundle, it will make it 1| inch thicker 
than the spindle is wide. The corners of these are taken 
off to a half round, and they are tied to the spindle with 
a small strong cord. These are to strike against the le- 
ver that works on a pin near its centre, which is fastened 
to the sieve, and shakes it as the trundle goes round ; 
(see it represented Plate XVIII.) This lever must al- 
ways be put to the side of the spindle, contrary to that 
of the meal spout; otherwise, it will draw the meal to the 
upper end of the sieve: there must be a spring fixed to 
the sieve to draw it forward as often as it is driven back. 
It must hang on straps and be fixed so as to be easily set 
to any descent required, by means of a roller in the form 
of a feeding screw, only longer; round this roller the 
strap winds. 

I have now given directions for making, and putting 
to work, all the machinery of one of the most complete 
of the old-fashioned grist-mills, that may do merchant- 
work in the small wav; these are represented by Plates 
XVIII., XIX., XX., XXI.; but they are far inferior to 
those with the improvements, which are shown by Plate 
XXII. 



CHAP. XXII.] OF THE USE OF DRAUGHT MILLS. 329 

CHAPTER XXII. 

ARTICLE 153. 
OF THE USE OF DRAUGHTING TO BUILD MILLS BY, &C. 

Perhaps some are of opinion that draughts are useless 
pictures of things, serving only to please the fancy. This 
is not what is intended by them; but to give true ideas 
of the machine, &c, described, or to be made. Those 
represented in the plates are all drawn on a scale |th 
of an inch to a foot, in order to suit the size of the book, 
except Plate XVII., which is a quarter of an inch to a 
foot; and this scale I recommend, as most buildings will 
then come on a sheet of common paper. 

N. B. Plate XXIV. was made after the above direc- 
tions, and has explanations to suit it. 

The great use of draughting mills, &c, to build by, 
is to convey our ideas more plainly than is possible by 
writing, or by words alone; these may be misconstrued 
or forgotten ; but a draught, well drawn, speaks for itself, 
when once understood by the artist; who, by applying 
his dividers to the draught and to the scale, finds the 
length, breadth, and height of the building, or the di- 
mensions of any piece of timber, and its proper place. 

By the draught, the bills of scantling, boards, rafters, 
lath, shingles, &c. &c, are known and made out; it 
should show every wheel, shaft, and machine, and their 
places. By it we can find whether the house be suffi- 
cient to contain all the works that are necessary to carry 
on the business; the builder or owner understands what 
he is about, and proceeds cheerfully and without error: 
it directs the mason where to put the windows, doors, 
navel-holes, the inner walls, &c, whereas, if there be no 
draught, every thing goes on, as it were, in the dark; 
much time is lost, and errors are committed to the loss of 
many pounds. I have heard a man say, that he believed 
his mill was 500/. better from having employed an expe- 
rienced artist to draw him a draught to build it by; and 
I know, by experience, the great utility of them. Every 
master builder, at least, ought to understand them. 



330 OF PLANNING AND DRAUGHTING MILLS. [CHAP. XXII. 



ARTICLE 154. 
DIRECTIONS FOR PLANNING AND DRAUGHTING MILLS. 

1st. If it be a new seat, view the ground where the 
dam is to be, and where the mill-house is to stand, and 
determine on the height of the top of the water in the 
head race, where it is taken out of the stream; and level 
from it for the lower side of the race, down to the seat 
of the mill-house, and mark the level of the water in the 
dam there. 

'2dly. Begin where the tajl-race is to empty into the 
stream, and level from the top of the water up to the mill 
seat, noticing the depth thereof, in places, as you pass 
along, which will be of use in digging it out. 

Then find the total fall, allowing one inch to a rod for 
fall in the races; but if they be very wide and long, less 
will do. 

Then, supposing the fall to be 21 feet 9 inches, which 
is sufficient for an overshot mill, and the stream too light 
for an undershot: consider well what size stone will suit; 
for I do not recommend a large stone to a weak, nor a 
small one to a strong stream. I have proposed stones 4 
feet diameter for light, 4,6 for middling, and 5 or 5 feet 
6 inches diameter, for heavy streams. Suppose you de- 
termine on stones 4 feet, then look in table I., (which is 
for stones of that size,) column 2, for the fall that is near- 
est 21 feet 9 inches, your fall, and you find it in the 7th 
example. Column 3d contains the head of water over the 
wheel, 3 feet; 4th, the diameter of the wheel, 18 feet ; 5th, 
its width, 2 feet 2 inches, &c, for all the proportions to 
make the stone revolve 106 times in a minute. 

Having determined on the size of the wheels, and aho 
of the house; the heights of the stories, to suit the wheels, 
and machinery it is to contain, and the business to be 
carried on therein, proceed to draw a ground plan of the 
house, such as plate XVIII., which is 32 by 55 feet. (See 
the description of the plate.) And for the second story, 
as plate XIX., &c, and for the 3d, 4th, and 5th floors, if 



CHAP. XXII.] BILLS OF SCANTLING. 331 

required ; taking care to plan every thing so that one 
shall not clash with another. 

Draw an end view, as Plate XX., and a side view, as 
Plate XXI. Take the draught to the ground, and stake 
out the seat of the house. It is, in general, best to set 
that corner of an overshot mill, at which the water en- 
ters, farthest in the bank ; but great care should be taken 
to reconsider and examine every thing, more than once, 
to see whether it be planned for the best; because, much 
labour is often lost for want of due consideration, and by 
setting buildings in, and laying foundations on, wrong 
places. The arrangements being completed, the bills of 
scantling and iron work may be made out from the 
draught. 



ARTICLE 155. 

BILLS OF SCANTLING FOR A MILL, 32 BY 55 FEET, 3 STORIES HIGH; 
THE WALLS OF MASON WORK, SUCH AS IS REPRESENTED IN PLATES 
XVIII. j XIX., XX., AND XXI. 

For the first Floor. 

2 sills, 29 feet long, 8 by 12 inches, to lay on the walls 

for the joists to lie on. 
48 joists, 10 feet long, 4 by 9 inches, all of timber that 

will last well in damp places. 

For the second Floor. 

2 posts, 9 feet long, 12 by 12 inches. 
2 girders, 30 feet long, 14 by 16 do. 
48 joists, 10 feet long, 4 by 9 do. 

For thejloor over the Water-house. 

1 cross girder, 30 feet long, 12 by 14 inches, for one end 
of the joists to lie on. 

2 posts to support the girder, 12 feet long, 12 by 12 

inches. 
16 joists, 13 feet long, 4 by 9 inches; all of good white- 
oak, or other timber, that will last in damp places. 



332 BILLS OF SCANTLING. [CHAP. XXII. 

For the third floor. 

4 posts, 9 feet long, 12 by 12 inches to support the gir- 
ders. 

2 girder posts, 7 feet long, 12 by 12 inches to stand on 
the water-house. 

2 girders, 53 feet long, 14 by 16 inches. 

90 joists, 10 feet long, 4 by 9 inches. 

For the fourth floor. 

6 posts, 8 feet long, 10 by 10 inches, to support the gir- 
ders. 

2 girders, 50 feet long, 13 by 15 inches. 

30 joists, 10 feet long, 4 by 8 do. for the middle tier of 
the floor. 

60 do. 12 feet do. 4 by 8, for the outside tiers, which ex- 
tends 12 inches over the walls, for the rafters to stand 
on. 

2 plates, 54 feet long, 3 by 10 inches: these lie on the top 
of the walls, and the joists on them. 

2 raising pieces, 55 feet long, 3 by 5 inches; these lie on 
the ends of the joists for the rafters to stand on. 

For the Roof. 

54 rafters, 22 feet long, 3 inches thick, 6| wide at the 

bottom, and 4| at the top end. 
25 collar beams, 17 feet long, 3 by 7 inches. 
2760 feet of laths, running measure. 
7000 shingles. 

For doors and Window-Cases? 

12 pieces, 12 feet long, 6 by 6 inches, for door-cases. 
36 do. 8 feet long, 5 by 5 inches, for window-cases. 

For the Water-House. 

2 sills, 27 feet long, 12 by 12 inches. 

1 do. 14 feet long, 12 by 12 do. 

2 spur-blocks, 4 feet 6 inches long, 7 by 7 do. 
2 head-blocks, 5 feet long, 12 by 14 do. 

4 posts, 10 feet long, 8 by 8, to bear up the penstock. 
2 cap-sails, 9 feet long, 8 by 10, for the penstock to stand 
on. 



CHAP. XXII.] BILLS OF SCANTLING. 333 

4 corner posts, 5 feet long, 4 by 6 inches, for the corners 
of the penstock. 

For the Husk of a Mill of one Water- Wheel and two pairs 

of Stones. 

2 sills, 24 feet long, 12 by 12 inches. 
4 comer posts, 7 feet long, 12 by 14 inches. 
2 front posts, 8 feet long, 8 by 12 do. 
2 back posts, 8 feet do. 10 by 12 inches, to support the 
back ends of the bridge-trees. 

2 other back posts, 8 feet long, 8 by 8 inches. 

3 tomkin posts, 12 feet long, 12 by 14 do. 

2 interties, 9 feet long, 12 by 12 inches, for the outer ends 

of the little cog-wheel shafts to rest on. 
2 beams, 24 feet long, 16 by 16 inches. 
2 bray- trees, 8| feet long, 6 by 12 inches. 
2 bridge-trees, 9 feet long, 10 by 10 inches. 

4 planks, 8 feet long, 6 by 14 inches, for the stone-bearers. 
20 planks, 9 feet long, 4 by about 15 inches, for the top 

of the husk. 

2 head-blocks, 7 feet long, 12 by 15 inches, for the wal- 
lower shafts to run on. They serve as spurs also for 
the head-block for the water-wheel shaft. 

For the Water- Wheel and big Cog-wheel. 

1 shaft, 18 feet long, 2 feet diameter. 

8 arms for the water wheel, 18 feet long, 3 by 9 inches. 
16 shrouds, 8§ feet long, 2 inches thick, and 8 deep. 
16 face boards, 8 feet long, 1 inch thick, and 9 deep. 
56 bucket boards, 2 feet 4 inches long, and 17 inches wide. 
140 feet of boards, for soaling the wheel. 

3 arms for the cog-wheel, 9 feet long, 4 by 14 inches. 
16 cants, 6 feet long, 4 by 17 inches. 

For little Cog-Wheels. 

2 shafts, 9 feet long, 14 inches diameter. 

4 arms, 7 feet long, 3| by 10 inches. 
16 cants, 5 feet long, 4 by 18 inches. 



334 BILL OF THE LARGE IRONS, &C. [CHAP. XXII. 

For Wallowers and Trundles. 

60 feet of plank, 3| inches thick. 

40 feet do. 3 inches thick, for bolting gears. 

Cogs and Rounds. 

200 cogs, to be split, 3 by 3, 14 inches long. 

80 rounds, do. 3 by 3, 20 inches long. 

160 cogs, for bolting works, 7 inches long, and If square; 

but if they be for a mill with machinery complete, there 

must be more in number, accordingly. 

Bolting Shafts. 

1 upright shaft, 14 feet long, 5| by 5| inches. 

2 horizontal shafts, 17 feet long, 5 by 5 inches. 
1 upright do. 12 feet long, 5 by 5 inches. 

6 shafts, 10 feet long, 4 by 4 do. 



ARTICLE 156. 
BILL OF THE LARGE IRONS FOR A MILL OF TWO PAIRS OF STONES. 

2 gudgeons, 2 feet 2 inches long in the shaft; neck 4| 

inches long, 3 inches diameter, well steeled and turned. 

(See fig. 16, Plate XXIV.) 
2 bands, 19 inches diameter inside, | thick; and 3 inches 

wide, for the ends of the shaft. 
2 do. 20| inches inside, \ an inch thick, and 2| inches 

wide, for do. 
2 do. 23 inches do. f an inch thick, and 2| inches wide, 

for do. 
4 gudgeons, 16 inches in the shaft, 3| inches long, and 

2~ inches diameter in the neck, for wallower shafts ; 

(See fig. 15, Plate XXIV.) 
4 bands, 12 inches diameter inside, ~ an inch thick, and 

2 wide, for do. 
4 do. 12 inches do. \ an inch thick, and 2 wide, for do. 
4 wallower bands, 3 feet 2 inches diameter inside, 3 

inches wide, and | of an inch thick. 
4 trundle bands, 2 feet diameter inside, 3 inches wide, 

and \ of an inch thick. 



CHAP. XXII.] BILL OF IRON. 335 

2 spindles and rynes; spindles 5 feet 3 inches long from 
the foot to the top of the necks; cock-heads 7 or 8 
inches long above the necks; the body of the spindles 
3| by 2 inches; the neck 3 inches long, and 3 inches di- 
ameter; the balance rynes proportional to the spindles, 
to suit the eye of the stone, which is 9 inches diameter. 
(See fig. 1,2, 3, Plate XXIV.) 

2 steps for the spindles, fig. 4. 

2 sets of damsel-irons, 6 knockers to each set. 

2 bray-irons, 3 feet long, If inch wide, § an inch thick: 
being a plain bar, one hole at the lower, and 5 or 6 at 
the upper end. 

Bill of Iron for the Bolting and Hoisting Works, in the 
common way. 

2 spur-wheel bands, 20 inches diameter from outsides 
for the bolting spur-wheel, f ths of an inch wide, and 
ith thick. 

2 spur-wheel bands, 12 inches diameter from outsides, 
for the hoisting spur-wheel. 

2 step-gudgeons and steps, 10 inches long, 1| inch thick 
in the tang or square part; neck 3 inches long, for the 
upright shafts. (See fig. 5 and 6, Plate XXIV.) 

2 bands for do. 5 inches diameter inside, 1± wide, and l\ 
thick. 

2 gudgeons, 9 inches tang; neck 3 inches long, 1| square 
for the top of the uprights. 

8 bands, 44 inches diameter inside. 

1 socket gudgeon, \\ of an inch thick; tang 12 inches 
long; neck 4 inches; tenon to go into the socket li 
inch, with a key-hole at the end. (See fig. 8 and 9.) 

14 gudgeons, neck 2i inches, tangs 8 inches long, and J 
inch square, for small shafts at one end of the bolting- 
reels. 

10 bands for do. 4 inches diameter inside, and 1 inch wide. 

4 socket-gudgeons, for the 4 bolting reels \~ square; 
tangs 8 inches; necks 3 inches, and tenons 1| inch 
with holes in the ends of the tangs for rivets, to keep 
them from turning ; the sockets one inch thick at the 
mortise, and 3' inches between the prongs. (See fig. 8 
and 9.) Prongs 8 inches long and 1 wide. 



336 EXPLANATION OF THE PLATES. [CHAP. XXII. 

8 bands, 3^ inches, and 8 do. 4 inches, diameter, for the 
bolting-reel shafts. 

For tlie Hoisting Wheels. 

2 gudgeons, for the jack-wheel, neck 3^ inches, and tang' 

9 inches long, 1-i square. 
2 bands for do. 41 inches diameter. 
2 gudgeons, for the hoisting wheel, neck 3| inches, tang 

9 inches long, and 11 inch square. 
2 bands for do. 7 inches diameter. 
6 bands for bolting-heads, 16 inches diameter inside, 2 J 

wide, and ith of an inch thick. 
6 do. for do. 15 inches do. do. 

N. B. All the gudgeons should taper a little, and the 
sides given are the largest part. The bands for shafts 
should be widest at the foremost side, to make them drive 
well; but those for heads should be both sides equal. Six 
picks for the stones, 8 inches long, and 1| wide, will be 
wanted. 



article 157. 

EXPLANATION OF THE PLATES. 

PLATE XVII. 

Drawn from a scale of a quarter of an inch for a foot. 
Fig. 1 — a big cog-wheel, 8 feet 2 J inches the diameter 

of its pitch circle, 8 feet 10^ inches from out to out: 

69 cogs, 4-| inches pitch. 
2 — a little cog-wheel, 5 feet 10J inches the diameter of 

its pitch circle, and 6 feet 6 inches from out to out, to 

have 52 cogs, 4\ pitch. 
3 — a wallower 3 feet 1| inch the diameter of its pitch 

circle, and 3 feet A\ inches from out to out; 26 rounds, 

41 pitch. 
4 — a trundle, 1 foot 8J inches the diameter of its pitch 

circle, and 1 foot 11J inches from out to out; 15 rounds, 

41 inches pitch. 
5 — the back part of the big cog-wheel. 



CHAP. XXII.] EXPLANATION OF THE PLATES. 337 

6 — a model of locking 3 arms together. 
7 — the plan of a forebay, showing the sills, caps, and 
where the mortises are made for the posts, with a rack at 
the upper end to keep off the trash. 

PLATE XVIII— The Ground Plan of a Mill. 

Fig. 1 and 8 — bolting chests and reels, top view. 

2 and 4 — cog-wheels that turn the reels. 

3 — cog-wheel on the lower end of a short upright shaft. 

5 and 7 — places for the bran to fall into. 

6, 6, 6 — three garners on the lower floor for bran. 

9 and 10 — posts to support the girders. 

1 1 — the lower door to load wagons, horses, &c, at. 

12 — the step-ladder, from the lower floor to the husk. 

13 — the place where the hoisting casks stand when filling. 

14 and 15 — the two meal-troughs and meal spouts. 

16 — meal-shaking sieve for Indian and buckwheat. 

17 — a box for the bran to fall into from the sieve. 

18 and 19 — the head-block and long spur-block, for the 
big shaft. 

20 — four posts in front of the husks, called bray posts. 

21 — the water and cog-wheel shaft. 

22 — the little cog-w T heel and shaft, for the lower stones. 

23 — the trundle for the burr stones. 

24 — the wallower for do. 

25 — the spur-wheel that turns the bolts. 

26 — the cog-wheel. 

27 — the trundle, head wallower, and bridge-tree, for coun- 
try stones. 

28 — the four back posts of the husk. 

29 — the two posts that support the cross-girder. 

30 — the two posts that bear up the penstock at one side. 

31 — the water wheel, 18 feet diameter. 

32 — the two posts that bear up the other side of the pen- 
stock. ^ 

33 — the head-blocks and spur-blocks, at water end. 

34 — a sill to keep up the outer ends. 

35 — the water-house door. 

36 — a hole in the wall for the trunk to go through. 

37 — the four windows of the lower story. 
22 



338 EXPLANATION OF THE PLATES. [CHAP. XXII. 

PLATE XIX.— Second floor. 

Fig. 1 and 9 — a top view of the bolting chests and reels. 

2 and 10 — places for the bran to fall into. 

3 and 8 — the shafts that turn the reels. 

4 and 7 — wheels that turn the reels. 

5 — a wheel on the long shafts between the uprights. 
6 — a wheel on the upper end of the upright shaft. 

11 and 12 — two posts that bear up the girders of the 
third floor. 

13 — the long shaft between two uprights. 

14 — five garners to hold toll, &c. 

15 — a door in the upper side of the mill-house. 

16 — a step ladder from 2d 'to 3d floor. 

17 — the running burr mill-stone laid off to be dressed. 

18 — the hatch-way. 

19 — stair- way. 

20 — the running country stone turned up to be dressed. 

21 — a small step-ladder from the husk to the 2d floor. 

22 — the places where the cranes stand. 

24 — the pulley-wheel that turns the rolling screen. 

25 and 26 — the shaft and wheel which turn the rolling 
screen and fan. 

27— the wheel on the horizontal shaft to turn two bolting 
reels. 

28 — the wheel on the upper end of the . first upright 
shaft. 

29 — a large pulley that turns the fan. 

30 — the pulley at the end of the rolling screen. 

31 — the fan. 

32 — the rolling screen. 

33 — a step ladder from the husk to the floor over the wa- 
ter-house. 

34 and 35 — two posts that support the girders of the 
third floor. 

36 — a small room for the tailings of the rolling screen. 

37 — a room for the fannings. 

3 Q — do. for the screenings. 

39 — a small room for the dust. 

40 — the penstock of water. 

41 — a room for the miller to keep his books in. 



CHAP. XXII.] EXPLANATION OF THE PLATES. 339 

42 — a fire-place. 

43 — the upper end door. 

44 — ten windows in the second story, twelve lights each. 

PLATE XX. 

Represents a view of the lower side of a stone mill- 
house, three stories high, which plan will suit tolerably 
well for a two story house, if the third story be not want- 
ed. Part of the wall is supposed to be open, so that we 
have a view of the stones, running gears, &c. 
Line 1 represents the lower floor, and is nearly level 

with the top of the sills, of the husk and water-house, 

2, 3, and 4 — the second, third, and fourth floors. 
5 and 6 — windows for admitting air under the lower 

floor. 
7 — the lower door, with steps to ascend to it, which com- 
monly suits best to load from. 
8 — the arch over the tail race for the water to run from 

the wheel. 
9 — the water-house door, which sometimes suits better to 

be at the end of the house, where it makes room to 

wedge the gudgeon. 
10 — the end of the water-wheel shaft. 
11 — the big cog-wheel shaft. 
12 — the little cog-wheel and wallower, the trundle being 

seen through the window. 
13 — the stones with the hopper, shoe, and feeder, as fixed 

for grinding. 
14 — the meal-trough. 

There is an end view of the husk frame. There are 
thirteen windows with twelve lights each. 

PLATE XXI. 

Represents an outside view of the water-end of a mill- 
house, and is intended to show to the builders and mill- 
wrights, the height of the walls, floors and timbers, with 
the places of the doors and windows, and a view of the 
position of the stones and husk timbers, supposing the 
w r all open, so that we could see them. 
Figs. 1, 2, 3, and 4, show the joists of the floors. 



340 OP SAW-MILLS. [chap. XXIII. 

5 — a weather-cock, turning on an iron rod. 

6 — the end of the shaft, for hoisting outside of the house, 
which is fixed above the collar beams over the doors, 
to hoist into either of them, or either story, at either 
end of the house, as may suit best. 

7 — the dark squares, showing the ends of the girders. 

8 — the joists over the water-house. 

9 — the mill-stones, with the spindles they run on, and 
the ends of the bridge-trees, as they rest on the brays 
aa. bb show the ends of the brays, that are raised and 
lowered by the levers cc, called the lighter-staffs, for 
raising and lowering the running stone. 

10 — the water-wheel and big cog-wheel. 

11 — the wall between the water and cog-wheel. 

12 — the end view of the two side walls of the house. 
Plate XXII. is explained in the preface. 



CHAPTER XXIII. 

V 

ARTICLE 158. 

OF SAW-MILLS. ' 

Construction of their Water Wheels. 

The wheels for saw-mills have been variously con- 
structed ; the most simple, where water is plenty, and the 
fall above six feet, is the flutter-wheel ; but where water 
is scarce, or the head insufficient to give flutter-wheels 
the requisite motion, high wheels, double-geared, will be 
found necessary. Flutter-wheels may be adapted to any 
head above six feet, by making them low and wide, fol- 
low heads, and high and narrow for high ones, so as to 
have about 120 revolutions, or strokes of the saw in a 
minute: but rather than double gear, I would be satisfied 
with 100. 



CHAP. XXIII.] 



OF SAW-MILLS. 



341 



A TABLE 



DIAMETER OF FLUTTER-WHEELS FROM OUT TO OUT, AND 
THEIR WIDTH IN THE CLEAR, SUITABLE TO ALL HEADS, 
FROM SIX TO THIRTY FEET. 



H 

CD 
SB 

O 

P 

Q 
*1 


b 

p' 
B 

CD 

CD 
•1 


Width. 


feet. 


ft. in. 


ft. in. 


6 


2: 8 


5: 6 


7 


2 : 10 


5 : 


8 


2: 11 


4:8 


9 


3 : 


4:3 


10 


3 : 1 


4: 


11 


3: 2 


3 : 9 


12 


3 : 3 


3 : 6 


13 


3:4 


3 : 3 


14 


3 : 5 


3 : 


15 


3: 6 


2: 9 


16 


3: 7 


2 : 6 


17 


3 : 8 


2: 4 


18 


3 : 9 


2: 2 


19 


3 : 10 


2 : 


20 


3 : 11 


1 : 10 


21 


4 : 


1 : 9 


22 


4 : 1 


1 : 8 


23 


4: 2 


1 : 7 


24 


4 : 3 


1 : 6 


25 


4 :4 


1 : 5 


26 


4: 5 


1 : 4 


27 


4 : 6 


1 : 3 


28 


4 : 7 


1 : 2 


29 


4 : 8 


1 : 1 


30 


4 : 9 


1 : 



N.B. — The above wheels are proposed to be made as narrow as will well do, 
on account of saving water; but if this be abundant, the wheels may be made 
\vider than directed in the table, and the mill will be the more powerful. 



342 OF SAW-MILLS. [CHAP. XXIII. 



Of Geared Saw-Mills. 

Of these I shall say but little, they being expensive 
and but little used. — They should be geared so as to give 
the saw 120 strokes in a minute, when at work in a com- 
mon log. The water-wheel is like that of any other 
mill, whether of the overshot, undershot, or breast kind; 
the cog-wheel of the spur kind, and as large as will clear 
the water. The wallower commonly has 14 or 1 5 rounds, 
or such number as will produce the right motion. On 
the wallower shaft is a balance-wheel, which may be 
made of stone or wood; this is to regulate the motion. 
There should be a good heatd above the water wheel to 
give it a lively motion, otherwise the mill will run hea- 
vily. 

The mechanism of a complete saw-mill is such as to 
produce the following effects; namely: — 

1. To move the saw up and down, with a sufficient 
motion and power. 

2, To move the log to meet the saw. 

,.3. To stop of itself when within 3 inches of being 
through the log. 

4. To draw the carriage with the log back, by the 
power of the water, so that the log may be ready to en- 
ter again. 

The mill is stopped as follows; namely: — When the 
gate is drawn the lever is held by a catch, and there is 
a trigger, one end of which is within half an inch of the 
side of the carriage, on which is a piece of wood an inch 
and a half thick, nailed so that it will catch against the 
trigger as the carriage moves, which throws the catch off 
the lever of the gate, and it shuts down at a proper time. 

Description of a Saw-Mill. 

Plate XXIII. is an elevation and perspective view of 
a saw-mill, showing the foundation, walls, frame, &c, &c. 

Fig. 0, 1 — the frame uncovered, 52 feet long, and 12 
feet wide. 

Fi°\ 2 — The lever for communicating the motion from 



CHAP. XXIII.] OP SAW-MILLS. 343 

the saw-gate to the carriage, to move the log ; it is 8 feet 
long, 3 inches square, tenoned into a roller 6 inches 
diameter, reaching from plate to plate, and working on 
gudgeons in them; in its lower side is framed a block, 10 
inches long, with a mortise in it two inches wide through- 
out its whole length, to receive the upper end of the hand 
pole, having in it several holes for an iron pin, to join 
the hand pole to it, to regulate the feed ; by setting the 
hand pole nearer the centre of the roller, less feed is given, 
and, farther off, gives more. 

Fig. 3, the hand pole or feeder, 12 feet long and 3 
inches square, where it joins the block, (Fig. 4,) and 
tapering 2 inches at the lower end, on which is the iron 
hand, 1 foot long, with a socket, the end of this is flat- 
tened, steeled, and hardened, and turned down half an 
inch at each side, to keep it on the rag-wheel. 

Fig. 5 — the rag-wheel. This has four cants, 4| feet 
long, 17 by 3 inches in the middle, lapped together to 
make the wheel 5 feet diameter; is faced between the 
arms with 2 inch plank, to strengthen the laps. The 
cramp or ratchet iron is put on as a hoop, nearly 1 inch 
square, with ratchet notches cut on its outer edge, about 
3 to an inch. On one side of the wheel are put 12 strong 
pins, 9 inches long, to tread the carriage back, when the 
backing works are out of order. On the other side are 
the cogs, about 56 in number, 3 inches pitch, to gear into 
the cog-wheel on the top of the tub-wheel shaft, with 15 
or 16 cogs. In the shaft of the rag-wheel are 6 or 7 
rounds, 11 inches long in the round part, let in nearly 
their whole thickness, so as to be of a pitch equal to the 
pitch of the cogs of the carriage, and gear into them easily: 
the ends are tapered off outside, and a band is driven on 
them at each end, to keep them in their places. 

Fig. 6 is the carriage ; a frame 4 feet wide from out- 
sides, one side 29 feet long, 7 by 7 inches; the other 32 
feet long, 8 by 7 inches, very straight and true, the in- 
terties at each end 15 by 4 inches, strongly tenoned and 
braced into the sides to keep the frame from racking. In 
the underside of the largest piece are set two rows of 
cogs, 2 inches between the rows, and 9 inches from the 



344 OF SAW-MILLS. [CHAP. XXIII. 

fo reside of one cog to that of another ; the cogs of one row 
between those of the other, so as to make 4| inches pitch, 
to gear into the rounds of the rag-wheel. The cogs are 
about 66 in number; shank 7 inches long, If inch square; 
head 2f long, 2 inches thick at the points, and 21 inches 
at the shoulder. 

Fig. 7 — the ways for the carriage to run on. These 
are strips of plank 4§ inches wide, 2 inches thick, set on 
edge, let 1 § inch into the top of the cross sills, of the 
whole length of the mill, keyed fast on one side, made 
very straight both side and edge, so that one of them will 
pass easily between the rows of cogs in the carriage, 
and leave no room for it to move sidewise. They should 
be of hard wood, well seasoned, and hollowed out between 
the sills to keep the dust from lodging on them. 

Fig. 8 — the fender posts. The gate with the saw 
plays in rabbets 2| deep and 4 inches wide, in the fen- 
der posts, which are 12 feet long, and 12 inches square, 
hung by hooked tenons to the front side of the two large 
cross beams in the middle of the frame, in mortises in 
their upper sides, so that they can be moved by keys to 
set them plumb. There are 3 mortises, 2 inches square, 
through each post, within half an inch of the rabbets, 
through which pass hooks with large heads, to keep the 
frame in the rabbets : they are keyed at the back of the 
posts. 

Fig. 9 — the saw, which is 6 feet long, 7 or 8 inches 
wide, when new; hung in a frame 6 feet wide from the 
outsides, 6 feet 3 inches long between the end pieces, the 
lowermost of which is 14 by 3 inches, the upper one 12 
by 3, the side pieces 5 by 3 inches, 10 feet long, all of the 
best dry, hard wood. The saw is fastened in the frame 
by two irons, in form of staples; the lower one with two 
screw pins passing through the lower end, screwing one 
leg to each side of the end piece : the legs of the upper 
one are made into screws, one at each side of the end 
piece, passing through a broad, flat bar, that rests on 
the top of the end piece, with strong burrs, li inch 
square, to be turned by an iron spanner, made to fit 
them. 



CHAP. XXIII.] OF SAW-MILLS. 345 

These straps are made of flat bars, 3 feet 9 inches long, 
3 inches wide, iths thick before turned ; at the turn they 
are 5 inches wide, square, and split to receive the saw 
and lug pins, then brought near together, so as to fit the 
gate. The saw is stretched tightly in this frame, by the 
screws at the top; exactly in the middle, at each end, 
measuring from the outside; the top end standing about 
half an inch more forward than the bottom. 

Fig. 10 — the forebay of water, projecting through the 
upper foundation wall. 

Fig. 11 — the flutter-wheel. Its diameter and length 
according to the head of water, as shown in the table. 
The floats are fastened in with keys, so that they will 
drive inward, when any thing gets under them, and not 
break. These wheels should be very heavy, that they 
may act as a fly, or balance, to regulate the motion, and 
work more powerfully. 

Fig, 12 — the crank, (see it represented by a draught, 
from a scale of 1 foot to an inch, fig. 17, Plate XXIV.) 
The part in the shaft 2 feet 3 inches long, 3| by 2 inches, 
neck 8 inches long, 3 thick, and 12 inches from the cen- 
tre of the neck to the centre of the wrist or handle, 
which is 5 inches long to the key hole, and 2 inches 
thick. 

The gudgeon at the other end of the shaft is 18 inches 
in the shaft, neck 3i long, 2| diameter. 

The crank is fastened in the same way as gudgeons. 
(See Art. 132.) 

Fig. 12, 13 — the pitman, which is 3| inches square 
at the upper end, 4| in the middle, and 4 near the loAver 
end ; but 20 inches of the lower end is 41 by 5|, to hold 
the boxes and key, to keep the handle of the crank tight. 



Pitman Irons of an improved Construction. 

(See fig. 10, 11, 12, 13, 14, 18, Plate XXIV.) Fig. 
10 is a plate or bar, with a hole in each end, through 
which the upper ends of the lug-pins 11 — 11 pass, with 
a strong burr screwed on each; they are 17 inches long, 



346 OP SAW-MILLS. [chap. XXIII. 

1| inch square, turned at the lower end to make a round 
hole 1| diameter; made strong round the hole. 

Fig. 12 is a large, flat link, through a mortise near the 
lower side of the end of the saw frame. The lug-pins 
pass one through each end of this link, which keeps them 
close to the gate sides. 

Fig. 14 is a bar of iron 2 feet long, 3| inches wide, \ 
inch thick at the lower, and 1| at the upper end. It is 
split at the top and turned as in the figure, to pass through 
the lug-pins. At fig. \ 3 there is a notch set in the head 
of the pitman bar 14, 1^ inch long, nearly as deep as to be 
in a straight line with the lower side of the side-pins, 
made a little hollow, steeled and made very hard. 

Fig. 18 is an iron plate, ,1-| inch wide, half an inch 
thick in the middle, with 2 large nail-holes in each end, 
and a round piece of steel welded across the middle and 
hardened, made to fit the notch in the upper end of the 
pitman, Plate XXVI., and draw close to the lug-pins, to 
the under side of the saw-frame, and nailed fast. Now, 
if the bearing part of this joint be in a straight line, the 
lower end of the pitman may play without friction in the 
joint, because both the upper and lower parts will roll 
without sliding, like the centre of a scale-beam, and will 
not wear. 

This is the best plan for pitman irons with which I am 
acquainted. The first set, so made, has been in my saw- 
mill 8 years, doing much hard work, and three minutes 
have not been required to adjust them. 

Fig. 14 — the tub-wheel, for running the carriage back. 
This is a very light wheel, 4 feet diameter, and put in 
motion by means of the foot or hand, at once throwing it 
in gear with the rag-wheel, lifting off the hand and clicks 
from the ratchet, and hoisting a little gate to let water on 
the wheel. The moment the saw stops, the carriage 
begins to move gently back again with the log. 

Fig. 15 — the cog-wheel on the top of the tub-wheel 
shaft, with 15 or 16 cogs. 

. Fig. 16 — the log on the carriage, sawed partly 
through. 

Fig. 17 — a crank and windlass, to increase power, by 









CHAP. XXIII.] OF SAW-MILLS. 347 

which one man can draw heavy logs on the mill, and turn 
them, by a rope passing round the log and windlass. 

Fig. 18 — a cant hook for rolling logs. 

Fig. 19 — a double dog, fixed into the hindmost head- 
block, used by some to hold the log. 

Fig. 20 — are smaller dogs to use occasionally at either 
end. 

Figs. 21, 22, represent the manner of shuting water on 
a flutter-wheel by a long, open shute, which should not 
be nearer to a perpendicular than an angle of 45 degrees, 
lest the water should rise from the shute and take air, 
which would cause a great loss of power. 

Fig. 23 represents a long, perpendicular, tight shute; the 
gate 23 is always drawn fully, and the quantity of water 
regulated at the bottom by a little gate r, for the purpose. 
There must be air let into this shute by a tube entering 
at a. (See Art. 71.) These shutes are for saving expense 
where the head is great, and should be much larger at the 
upper than at the lower end, else there will be a loss of 
power. They must be very strong, otherwise they will 
burst. The perpendicular ones suit best where a race 
passes within 12 feet of the upper side of the mill. 



OPERATION. 

The sluice drawn from the penstock 1 0, puts the wheel 
11 in motion — the crank 12 moves the saw-gate, and saw 
9, up and down, and as they rise they lift up the lever 
2, which pushes forward the hand-pole 3, which moves 
the rag-wheel 5, which gears in the cogs of the carriage 
4, and draws forward the log 16 to meet the saw, as much 
as is proper to cut at a stroke. When it is within 3 
inches of being through the log, the cleet C, on the side 
of the carriage, arrives at a trigger and lets it fly, and 
the sluice gate shuts down ; the miller instantly draws 
water on the wheel 14, which runs the log gently back, 
&c. 



348 OF A FULLING-MILL. [CHAP. XXIII. 

ARTICLE 159. 

DESCRIPTION OF A FULLING-MILL. 

Fig. 19, Plate XXIV., is the penstock, water-gate, and 
spout of an overshot fulling-mill, the whole laid down 
from a scale of 4 feet to an inch. 

Fig. 20 — one of the 3 interties, that are framed with 
one end into the front side of the top of the stock-block; 
the other ends into the tops of the 3 circular pieces that 
guide the mallets; they are 6 feet long, 5 inches wide, 
and 6 deep. 

Fig. 21 are two mallets: they are 4 feet 3 inches long, 
21 inches wide, and 8 thick, shaped as in the figure. 

Fig. 22 — their handles, 8 feet long, 20 inches wide, and 
3 thick: a roller passes through them, 8 inches from the 
upper ends, and hangs in the hindermost corner of the 
stock-post. The other ends go through the mallets, and 
have each, on their underside, a plate of iron faced with 
steel and hardened, 2 feet long, 3 inches wide, fastened 
by screw-bolts, for the tappet-blocks to rub against while 
lifting the mallets. 

Fig. 23 — the stock-post, 7 feet long, 2 feet square at the 
bottom, 15 inches thick at the top, and shaped as in the 
figure. 

Fig. 24 — the stock where the cloth is beaten, shaped 
inside as in the figure, planked inside as high as the dotted 
line, which planks are put in rabbets in the post, the inside 
of the stock being 18 inches wide at the bottom, 19 at the 
top, and 2 feet deep. 

Fig. 25 — one of the 3 circular guides for the mallets; 
they are 6 feet long, 7 inches deep, and 5 thick; are 
framed into a cross sill at bottom, that joins its lower edge 
to the stock-post. This sill forms a part of the bottom 
of the stock, and is 4 feet long, 20 inches Avide, and 10 
thick. 

The sill under the stock-post is 6 feet long, 20 inches 
wide, and 18 thick. The sill before the stock is 6 feet 
long, and 14 inches square. 

Fig. 26 — the tappet-arms, 5 feet 6 inches long, 21 






CHAP. XXIII.] OF A FULLING-MILL. 349 

inches each side of the shaft, 12 inches wide and 4 thick. 
There is a mortise through each of them, 4 inches wide, 
the length from shaft to tappet, for the ends of the mal- 
let handles to pass through. The tappets are 4 pieces 
of hard wood, 12 inches long, 5 wide and 4 thick, made 
in the form of half circles pinned to the ends of the 
arms. 

Fig. 27 — an overshot water-wheel, similar to those in 
other mills. 

Fig. 28 — one of the 3 sills, 16 feet long, and 16 inches 
square with walls under them, as in the figure. 

OPERATION. 

The cloth is put in a loose heap in the stock 24; the 
water being drawn on the wheel, the tappet-arms lift the 
mallets, alternately, which strike the under part of the 
heap of cloth, and the upper part is continually falling 
over, and thereby turning and changing its position under 
the mallets, which are shaped as in the figure, to produce 
this effect. 

Descriptions of the Drawings of the Iron-work, Plate XXIV, 

Fig. 1 is a spindle, 2 the balance-ryne, and 3 the driver, 
for a mill-stone. The length of the spindle from the foot 
to the top of the neck is about 5 feet 3 inches; cock-head 
8 or 9 inches from the top of the neck, which is 3 inches 
long, and 3 diameter; blade or body 3^ by 2 inches; foot 
\\ inch diameter; the neck, foot and top of the cock- 
head, steeled, turned, and hardened. 

Fig. 2— the balance-ryne is sometimes made with 3 
horns, one of which is so short as only to reach to the top 
of the driver, which is let into the stone directly under 
it ; the other to reach nearly as low as the bottom of the 
driver : of late, they are mostly made with 2 horns only; 
this may be made sufficiently fast by making it a little 
wider than the eye, and letting it into the stone a little 
on each side, to keep it steady and prevent its moving 
sidewise. Some choose them with 4 horns, which fill 
the eye too much. 



350 OF SAW-MILLS. [CHAP. XXIII. 

Fig. 3 is a driver, about 15 inches long. 

Fig. 4 — the step for the spindle foot to run in. It is 
a box 6 inches long, 4 inches wide at the top, but less at 
bottom, and 4 inches deep outside, at the sides and bot- 
tom half an inch thick. A piece of iron 1 inch thick is 
fitted to lie tightly in the bottom of this box, but not weld- 
ed: in the middle of this is welded a plug of steel If inch 
square, in which is punched a hole a quarter of an inch 
deep, to fit the spindle foot. The box must be tight, to 
hold oil. 

Fig. 5 — a step-gudgeon for large upright shafts, 16 
inches long, and 2 square, steeled and turned at the toe. 

Fig. 6— the step for it, similar to 4, but proportionably 
less. ( 

Fig. 7 is a gudgeon for large bolting shafts, 13 inches 
lono - , and If square. 

Fig. 8 — a large joint-gudgeon, tang 14 inches, neck 5 
and tenon 2 inches long, 1 \ square. 

Fig. 9 — the socket part to fit the shafts, with 3 rivet- 
holes in inch. 

Fig. 10, 14, 18 — pitman irons, described Art. 158. 

Fig. 15, the wallower gudgeon, tang 16 inches, neck 
3§* inches long, and 21 diameter. 

Fig. 16 — the water-wheel gudgeon, tang 3 feet 2 inches 
long, neck A\ inches long, 31 square. 

Fig. 17 — a saw-mill crank, described Art. 158. 

N.B. — The spindle-ryne, &c, is drawn from a scale 
of 2 feet to an inch, and all the other irons 1 foot to an 
inch. 



article 160. 

To what has been said of Saw-mills, by Thomas Elli 
cott, I add the following: — 

Of hanging the Saiu. 
First, set the fender posts as nearly plumb every way 
as possible, and the head-blocks on which the log is to 
lie level. Put the saw just in the middle of the gate, 



CHAP. XXIII.] OF SAW-MILLS. 351 

measuring from the outsides, set it by the gate and not 
by a plumb line, with the upper teeth about half an inch 
farther forward than the lower ones: — this is to give the 
saw liberty to rise without cutting, and the log room to 
push forward as it rises. Run the carriage forward so 
that the saw may strike the block — strike up a nail, &c, 
then run it back again its full length, and standing be- 
hind the saw, set it to direct exactly to the mark. Stretch 
the saw in the frame, rather the most at the edge, that it 
may be stifTest there. Set it in motion, and hold a tool 
close to one side of it, and observe whether it touch equal, 
the whole length of the stroke — try if it be square with 
the top of the head-blocks, else it will not make the scant- 
ling square. 

Of Whetting the Saw. 

The edge of the teeth ought to be kept straight, and 
not suffered to wear hollowing — set the teeth a little out 
equal at each side, and the outer corners a little longest; 
they will then clear their way. Some whet the under 
side of the teeth nearly level, and others a little drooping 
down, but it then never saws steadily, but is apt to wood 
too much; the teeth should slope up, although but very 
little. Try a cut through the log, and if it come out at 
the mark made to set it by, it is shown to be hung right. 

Of Springing Logs Straight. 

Some long small logs will spring so much in sawing as 
to spoil the scantling, unless they can be held straight; 
to do which make a clamp to bear with one end against 
the side of the carriage, the other end under the log, with 
a post up the side thereof — drive a wedge between the 
post and log, and spring it straight; this will bend the 
carriage side — but this is no injury. 

Of moving the Logs to the size of the Scantling, §c. 

Make a sliding-block to slide in a rabbet in front of 
the main head-block; fasten the log to this with a little 
dog on each side, one end of which being round, is driven 
into a round hole, in the front side of the sliding-block, 



352 OF SAW-MILLS. [CHAP. XXIII. 

the other flattened to drive in the log, cutting across the 
grain, slanting a little out — it will draw the log tight and 
stick in it the better. Set a post of hard wood in the 
middle of the main block close to the sliding one, and to 
extend with a shoulder over the sliding one, for a wedge 
to be driven under this shoulder to keep the block tight. 
Make a mark on each block to measure from — when the 
log is moved the key is driven out. The other end next 
the saw is best held by a sliding dog, part on each side 
of the saw, pointed like a gouge, with two joint dogs, one 
on each side of the saw. 

Remedy for a long Pitman. 

Make it in two parts by a joint 10 feet from the crank, 
and a mortise through a fixed beam, for the lower end of 
the upper part to play in ; the gate will work more steadily, 
and all may be made lighter. 

The feed of a saw-mill ought to be regulated by a screw 
fixed to move the hand-pole nearer or farther from the 
centre of the roller that moves it, which may be done, 
as the saw arrives at a knot without stopping the mill. 



article 161. 

The following Observations on Saw- Mills, fyc, were com- 
municated by William French, Mill- Wright, New Jersey. 

Saw-mills, with low heads, have been much improved 
in this state. Mills with two saws, with not more than 
7 feet head and fall, have sawed from five to six hundred 
thousand feet of boards, plank, and scantling, in one year. 
If the water be put on the wheel in a proper manner, 
and the wheel of a proper size, (as by the following ta- 
ble,) the saw will strike between 100 and 130 strokes in 
a minute, (see fig. 1, Plate XXVI.) The lower edge of 
the breast-beam B to be |ths the height of the wheel, 
and one inch to a foot, slanting up stream, fastened to 
the penstock posts with screw-bolts, (see post A) circled 



CHAP. XXIII.] OF SAW-MILLS. 353 

out to suit the wheel C ; the fall A circled to suit the 
wheel and extending to F, 2 inches above the lower edge 
of the breast-beam, or higher, according to the size of the 
throat or sluice E, with a shuttle, or gate, sliding on F E, 
shutting against the breast-beam B: then 4 buckets out 
of 9 will be acted on by the water. The method of fas- 
tening the buckets or floats is, to step them in starts 
mortised in the shaft— see start G — 9 buckets in wheel 
4| inches wide, see them numbered 1, 2, &c. 

Fig. 2, the go back, is a tub wheel. Its common size 
is from 4| to 6 feet diameter, with 16 buckets. The 
water is brought on it by the trunk H. The bucket I, 
is made with a long tenon, so as to fasten it with a pin 
at the top of the wheel. 

TABLE. 

Of the Dimensions of Flutter-wheels. 



Head 12 


feet. 


B 


acket 5 feet. 


Wheel 


3 feet. 


Throat 1£ inches 


11 






H 




3 


2 


10 






6 




3 


2 1-8 


9 






*h 




2 10 inches. 


2* 


8 






7 




2 9 


% 


7 






u 




2 8 


3i 


G 






8 




2 7 p. 


3i 


5 






9 




2 6 


31 



N. B. — The crank about 11 inches, but varies to suit the timber. 

The Pile Engine. 

Fig. 3, a simple machine for driving piles in soft bot- 
toms for setting mill-walls or dams on. It consists of a 
frame 6 or 7 feet square, of scantling, 4 by 5 inches, with 
2 upright posts 2 inches apart, 10 to 12 feet high, 3 by 3 
inches, brace from top to bottom of the frame, with a 
cap on top 2 feet long, 6 by 8 inches, with a pulley in its 
middle, for a rope to bend over, fastened to a block I, 
called a tup, which has 2 pieces, 4 inches wide between 
the uprights, with a piece of 2 inch plank T, 6 inches 
wide, framed on the ends, so as to slide up and down the 
upright posts S. This machine is worked by 4 or 6 men, 
who draw the tup up by the sticks fastened to the end of 
the rope K, and let it fall on the pile L; they can thus 
strike 30 or 40 strokes in a minute by the swing of their 
arms. 
23 



354 OF SAW-MILLS. [CHAP. XXIII. 



Of building Dams on soft Foundations. 

The best method is to lay 3 sills across the stream, and 
frame cross sills into them up and down stream, setting 
the main mud sills on round piles, and pile them with 2 
inch plank, well jointed, and driven closely together, 
edge to edge, from one end to the other. Taking one 
corner off the lower end of the plank will cause it to 
keep a close joint at bottom, and by driving an iron dog 
in the mud-sill, and a wooden wedge to keep it close at 
the top end, it will be held to its place when the tup 
strikes. It is necessary to pile the outside cross sills 
also in some bottoms, and to have wings to run 10 or 12 
feet into the bank at each side; and the wing-posts 2 or 
3 feet higher than the posts of the dam, where the water 
falls over, planked to the top N N, and filled with dirt to 
the plate O. 

Fig. 4 is a front view of the breast of the tumbling 
dam. 

Fig. 5 is a side view of the frame of the tumbling dam, 
on its piling abcde, and f g h is the end of the mud- 
sills. The posts k, are framed into the main mud-sills 
with a hook tenon, leaning down stream 6 inches in 7 
feet, supported by the braces 11, framed into the cross 
sills I; the cross sills I to run 25 feet up and down stream, 
and to be well planked over, and the breast-posts to be 
planked to the top, (see P, fig. 4,) and filled with dirt 
on the upper side, within 12 or 18 inches of the plate O, 
(see Q, fig. 5) slanting to cover the up-stream ends of 
the sills 3 or 4 feet deep; R represents the water. 

When the heads are high, it is best to plank the braces 
for the water to run down; but, if low, it may fall per- 
pendicularly on the sheeting. 



CHAP. XXIV.] THE PATH TO NEW INVENTIONS. 355 



CHAPTER XXIV. 

RULES FOR DISCOVERING NEW IMPROVEMENTS; EXEMPLIFIED IN IM- 
PROVING THE ART OF CLEANING AND HULLING RICE, WARMING 
ROOMS, VENTING SMOKE BY CHIMNEYS, &C* 

The true Path to Inventions. 

Necessity is called the mother of invention, but, upon 
inquiry, we shall find that Reason and Experiment bring 
it forth ; for almost all inventions have resulted from such 
steps as the following: — 

I. To investigate the fundamental principles of the 
theory, and process of the art, or manufacture, we wish 
to improve. 

II. To consider what is the best plan, in theory, that 
can be deduced from, or founded on, those principles, to 
produce the effect we desire. 

III. To inquire whether the theory be already put in 
practice to the best advantage; and what are the imper- 
fections or disadvantages of the common process, and 
what plans are likely to succeed better. 

IV. To make experiments in practice, upon any plans 
that these speculative reasonings may suggest, or lead to. 
Any ingenious artist, taking the foregoing steps, will pro- 
bably be led to improvement on his own art: for we see, 
by daily experience, that every art may be improved. 
It will, however, be in vain to attempt improvements, 
unless the mind be freed from prejudices in favour of 
established plans. 

EXAMPLE I. 

On the Art of cleaning Grain by Wind. 

I. What are the principles on which the art is founded ? 
When bodies fall through resisting mediums, their velo- 

* The rules and observations which formed an appendix to the former editions 
of this work, contain some suggestions which are worthy of attention. Since 
they were written many improvements have been made in the processes to which 
they refer ; but the path is still open, and perhaps the remarks made by Mr. Evans, 
may yet lead to useful results ; with this hope, they have, with some modifications, 
been retained. 



356 THE PATH TO NEW INVENTIONS. [CHAP. XXIY. 

cities are as their specific gravities, and the surface they 
expose to the medium; consequently, when light and 
heavy articles are mixed together, the farther they fall, 
the greater will be their distance apart : on this principle 
a separation can be effected. 

II. What is the best plan in theory? First, make a 
current of air, as deep as possible, for the grain to fall 
through ; the lightest will then be carried farthest, and 
the separation be more complete at the end of the fall. 
Secondly, cause the grain, with the chaff, &c, to fall in 
a narrow line across the current, that the light parts may 
meet no obstruction from the heavy in being carried for- 
ward. Thirdly, fix a moveable board edgewise to sepa- 
rate between the good clean, and the light grain, &c. 
Fourthly, cause the same blast to blow the grain several 
times, and thereby effect a complete separation at one 
operation. 

III. Is this theory in practice already? what are the 
disadvantages of the common process? We find that the 
farmers' common fans drop the grain in a line 15 inches 
wide ; to fall through a current of air about 8 inches deep, 
instead of falling in a line half an inch wide, through a 
current three feet deep; so that it requires a very strong^ 
blast even to blow out the chafT; but garlic, like grains, 
&c, cannot be thus removed, as they meet so much ob- 
struction from the heavy grains; the grain, has, therefore, 
to undergo two or three such operations, so that the prac- 
tice appears absurd, when tried by the scale of reason. 

IV. The fourth step is to construct a fan to put the 
theory in practice, by experiment. (See Art. 83.) 

EXAMPLE IL 

Hie Art of Distillation. 

I. The principles on which this art is founded, are 
evaporation and condensation. When liquid is heated, 
the spirit it contains, being more volatile than the watery 
part, evaporates, before it, into steam, which being con- 
densed again into a liquid, by cold, is obtained in a sepa- 
rate state. 



CHAP. XXIV.] THE PATH TO NEW INVENTIONS. 357 

II. The best plan, in theory, for effecting this, appears 
to be as follows ; the fire should be applied to the still, so 
as to spend the greatest possible part of its heat to heat the 
liquid. Secondly, the steam should be conveyed into a 
metallic vessel of any suitable form, and this should be im- 
mersed in cold water, to condense the steam : in order to 
keep the condenser cold, there should be a stream of cold 
water continually entering the bottom and flowing over 
the top of the condensing tub; the steam should have no 
free passage out of the condenser, else the strongest part 
of the liquor will escape. 

III. Is this theory already put in practice, and what 
are the disadvantages of the common process? — 1st, 
A great part of the heat escapes up the chimney. 2dly, 
It is almost impossible to keep the grounds from burning 
in the still. 3dly, The fire cannot be regulated to keep 
the still from boiling over; we are, therefore, obliged to 
run the spirit off very slowly; how are we to remedy 
these disadvantages? — First, to lessen the fuel, apply the 
lire as much to the surface of the still as possible; enclose 
the fire by a wall of clay that will not convey the heat 
away so fast as stone; let in no more air than is necessary 
to keep the fire burning, for the surplus air carries away 
the heat of the fire. Secondly, to keep the grounds from 
burning, immerse the still, with the contained liquor, 
in a vessel of water, joining their tops together; then, 
by applying the fire to heat the water in the outside 
vessel, the grounds will not burn, and by regulating the 
heat of the outside vessel the still may be kept from boil- 
ing over. 

IV. A still to be heated through the medium of water, 
was made, some years ago, by Colonel Alexander Ander- 
son, of Philadelphia, and the experiment tried; but the 
outside vessel being open, the water in it boiled away, 
and carried off the heat, and the liquor in the still could 
not be made to boil — this appeared to defeat the scheme. 
But, by enclosing the water in a tight vessel, so that the 
steam could not escape, and that the heat might be in- 
creased, it now passed to the liquor in the still, which 
boiled as well as if the fire had been immediately applied 
to it. By fixing a valve to be loaded so as to let the 



358 THE PATH TO NEW INVENTIONS. [CHAP. XXIV. 

steam escape, when it has arrived at such a degree of 
heat as to require it, all danger of explosion is avoided, 
and all boiling over prevented. 

EXAMPLE III. 

The Art of venting Smoke from Rooms by Chimneys, 

I. The principles are : — Heat, by repelling the parti- 
cles of air to a greater distance than when cold, renders 
it lighter than cold air, and it will rise above it, forming 
a current upwards, with a velocity proportional to the 
degree of heat, and the size of the tube or funnel of the 
chimney, through which it ascends, and with a power 
proportional to its perpendicular height; which power 
to ascend will always be equal to the difference of the 
weight of a column of rarefied air of the size of the small- 
est part of the chimney, and a column of common air of 
equal size. 

II. What is the best plan, in theory, for venting 
smoke, that can be founded on these principles? 

1st. The size of the chimney must be proportioned to 
the size and closeness of the room and to the fire; be- 
cause, if the chimney be immensely large, and the fire 
small, there will be little current upwards. And again, 
if the fire be large, and the chimney too small, the smoke 
cannot be all vented by it: more air being necessary to 
supply the fire, than can find vent up the chimney, it 
must spread in the room again, which air, after passing 
through the fire, is rendered deleterious. 

2dly. The narrowest place in the chimney must be 
next the fire, and in front of it, so that the smoke would 
have to pass under it to get into the room; the current 
will there be greatest, and will draw up the smoke 
briskly. 

3dly. The chimney must be perfectly tight, so as to 
admit no air but at the bottom. 

III. The errors in chimneys in common practice, are, 
1st. In making them widest at bottom. 

2dly. Too large for the size and closeness of the room. 

3dly. In not building them high enough, so that the 

wind, whirling over the tops of houses, blows down them. 



CHAP. XXIV.] THE PATH TO NEW INVENTIONS. 359 

4thly. By letting in air any where above the breast 
or opening, which destroys the current of it at the bot- 
tom. 

IV. The cures directed by the principles and theory, 
are, 

1st. If the chimney smoke on account of being too 
large for the size and closeness of the room, make the 
chimney less at the bottom — its size at the top may not 
do much injury, but it will weaken the power of ascent, 
by giving the smoke time to cool before it leave the chim- 
ney -, the room may be as tight, and the fire as small as 
you please, if the chimney be in proportion. 

2dly. If it be small at the top and large at the bottom, 
there is no cure but to lessen it at the bottom, 

3dly. If it be too small, which is seldom the case, stop 
up the chimney and use a stove — it will be large enough 
to vent all the air that can pass through a two inch hole, 
which is large enough to sustain the fire in a stove. 
Chimneys built in accordance with these theories, I be- 
lieve, are every where found to answer the purpose. 
(See Franklin's letters on smoky chimneys.) 

EXAMPLE IV. 

The art of warming Rooms by Fire, 

I. Consider in what way fire operates. 

1st. The fire heats and rarefies the air in the room, 
which gives us the sensation of heat or warmth. 

2dly. The warmest part of the air being lightest, rises 
to the uppermost part of the room, and will ascend 
through holes (if there be any) to the room above, making 
it warmer than the one in which the fire is, 

3dly. If the chimney be too open, the warm air will 
fly up it, leaving the room empty ; the cold air will then 
rush in at all crevices to supply its place, which keeps the 
room cold. 

II. Considering these principles, what is the best plan 
in theory, for warming rooms ? 

1st. We must contrive to apply the fire to spend all 
its heat, to warm the air which comes into the room. 



360 THE PATH TO NEW INVENTIONS. [CHAP. XXIV. 

2dly. The warm air must be retained in the room as 
long as possible. 

3dly. Make the fire in a lower room, conducting the 
heat through the floor into the upper one, and leaving 
another hole for the cold air to descend to the lower 
room. 

4thly. Make the room so tight as to admit no more 
cold air, than can be warmed as it comes in. 

5thly. By closing the chimney so as to let no warm air 
escape, but that which is absolutely necessary to sustain 
the fire — a hole of two square finches will be sufficient 
for a very large room. 

6thly. The fire may be supplied by a current of air 
brought from without, not qsing any of the air already 
warmed. If this theory, which is founded on true princi- 
ples and reason, be compared with common practice, the 
errors will appear, and may be avoided. 

I had a stove, constructed in accordance with these 
principles, and have found all to answer according to 
theory. 

The operation and effects are as follows ; namely : — 

1st. It applies the fire to warm the air as it enters the 
room, and admits a full and fresh supply, rendering the 
room moderately warm throughout. 

2dly. It effectually prevents the cold air from pressing 
in at the chinks or crevices, but causes a small current 
to pass outward. 

3dly. It conveys the coldest air out of the room first, 
consequently, 

4thly. It is a complete ventilator, thereby rendering 
the room healthy. 

5thly. The fire may be supplied (in very cold weather) 
by a current of air from without, that does not communi- 
cate with the warm air in the room. 

6thly. Warm air may be retained in the room any 
length of time, at pleasure; circulating through the stove 
the coldest entering first, to be warmed over again. 

7thly. It will bake, roast, and boil equally well with 
the common ten plate stove, as it has a capacious oven. 

8thly. In consequence of these improvements, it re- 
quires not more than half the usual quantity of fuel. 



CHAP. XXIV.] THE PATH TO NEW INVENTIONS. 361 

Description of the Philosophical and Ventilating Stove. 

It consists of three parts, either cylindrical or square, 
the greatest surrounding the least. (See fig. 1, Plate 
X.) S F is a perspective view thereof in a square form, 
supposed open at one side : the fire is put in at F, into 
the least part, which communicates with the space next 
the outside, where the smoke passes to the pipe 1 — 5. 
The middle part is about two inches less than the out- 
side part, leaving a large space between it, and above 
the inner part, for an oven in which the air is warmed, 
being brought in by a pipe B D between the joists of the 
floor, from a hole in the wall at B, it rises under the stove 
at D, into the space surrounding the oven and the fire, 
which air is again surrounded by the smoke flue, giving 
the fire a full action to warm it, whence it ascends into the 
room by the pipe 2. E brings air from the pipe D B to 
blow the fire. H is a view of the front end plate, showing 
the fire and oven doors. I is a view of the back end, the 
plate being off, the dark square shows the space for the 
fire, and the light part the air-space surrounding the fire, 
the dark outside space the smoke surrounding the air; 
these are drawn on a larger scale. The stove consists of 
fifteen plates, twelve of which join, by one end, against 
the front plate H. 

To apply this stove to the best advantage, suppose 
fig. 1, Plate X., to represent a three or four story house, 
two rooms on a floor — set the stove S F in the partition 
on the lower floor, half in each room; pass the smoke pipe 
through all the stories; make the room very close; let no 
air enter but what comes in by the pipes A B or G C 
through the wall at A and G, that it may be the more 
pure, and pass through the stove and be warmed. But 
to convey it to any room, and take as much heat as pos- 
sible with it, there must be an air-pipe surrounding the 
smoke pipe, with a valve to open at every floor. Sup- 
pose we wish to warm the rooms No. 3 — 6, we open the 
valves, and the warm air enters, ascends to the upper 
part, depresses the cold air, and if we open the holes a — c, 
it will descend the pipes, and enter the stove to be 
warmed again: this may be done in very cold weather. 



362 THE PATH TO NEW INVENTIONS. [CHAP. XXIV. 

The higher the room above the stove, the more power- 
fully will the warm air ascend and expel the cold air. 
But if the room require to be ventilated, the air must be 
prevented from descending, by shutting the little gate 
2 or 5, and drawing 1 or 6, and getting it liberty to as- 
cend and escape at A or G — or up the chimney, letting 
it in close at the hearth. If the warm air be conveyed 
under the floor, as between 5 — 6, and let rise in several 
places, with a valve at each, it will be extremely conve- 
nient and pleasant; if above the floor, as at 4, several per- 
sons might set their feet on it to warm. The rooms will 
be moderately warm throughout — a person will not be 
sensible of the coldness of the weather. 

One large stove of this construction may be made to 
warm a whole house, ventilate the rooms at pleasure, 
bake bread, meat, &c. 

These principles and improvements ought to be con- 
sidered and provided for in building. 

EXAMPLE V. 

Art of Hulling and Cleaning Rice. 

,Step I. The principles on which this art may be 
founded, will appear, by taking a handful of rough rice, 
and rubbing it hard between the hands — the hulls will 
be broken off, and, by continuing the operation, the 
sharp texture of the outside of the hull (which, through 
a magnifying glass, appears like a sharp, fine file, and 
no doubt, is designed by nature for the purpose) will 
cut off the inside hull, and the chaff being blown out, will 
leave the rice perfectly clean, without breaking any of 
the grains. 

II. What is the best plan in theory, for effecting this? 
(See the plan proposed, represented in Plate X., fig. 2; 
explained Art. 103.) 



CHAP. XXIV.] THE PATH TO NEW INVENTIONS. 363 

EXAMPLE VI. 

To save Ships from Sinking at Sea. 

Step I. The principle on which ships float, is the 
difference of their specific gravities from that of the wa- 
ter — sinking only to displace a quantity of water equal 
in weight to that of the ship and its lading; they sink 
deeper, therefore, in fresh than in salt water. If we can 
calculate the weight of the cubic feet of water a ship dis- 
places when empty, it will show her weight, and sub- 
tracting that from what she displaces when loaded, shows 
the weight of her load ; each cubic foot of fresh water 
weighing 62,5 lbs. If an empty rum hogshead weigh 
62,5 lbs, and measure 15 cubic feet, it will require 875 
lbs. to sink it. A vessel of iron, containing air only, and 
so large as to make its whole bulk lighter than so much 
water, will float, but if it be filled with water, it will sink. 
Hence, we may conclude, that a ship loaded with any 
thing that will float, will not sink if filled with water; 
but if loaded with any thing specifically heavier than wa- 
ter, it will sink as soon as filled. 

II. This appears to be the true theory: — How is it to 
be applied, in case a ship spring a leak, that gains on the 
pumps? 

III. The mariner who understands well the above prin- 
ciples and theory will be led to the following steps : 

1st. To cast overboard such things as will not float, 
and carefully to reserve every thing that will float, for 
by them the ship may at last be buoyed up. 

2dly. To empty every cask or thing that can be made 
water-tight, to put them in the hold, and fasten them 
down under the water, filling the vacancies between them 
with billets of wood; even the spars and masts, may, in des- 
perate cases, be cut up for this purpose, which will fill 
the hold with light matter, and as soon as the water in- 
side is level with that outside, no more will enter. If 
every hogshead buoy up 875 lbs., they will be a great 
help to buoy up the ship, (but care must be taken not to 
put the empty casks too low, which would overset the 
ship,) and she will float, although half the bottom be torn 



364 



THE PATH TO NEW INVENTIONS. [CHAP. XXIV. 



off. Mariners, for want of this knowledge, often leave 
their ships too soon, taking to their boats, although the 
ship be much the safest, and do not sink for a long time 
after being abandoned— not considering that, although 
the water gain on their pumps at first, they may be able 
to hold way with it when risen to a certain height in the 
hold, because the velocity with which it will enter, will 
be in proportion to the square root of the difference be- 
tween the level of the water inside and outside — added 
to this, the fuller the ship the easier the pumps will work, 
because the water has to be raised to a less height; there- 
fore, they ought not to be too soon discouraged. 



Description of the Thrashing Machine, with Elastic Flails; 
invented hy James Wardrop, of Ampthill, Virginia* 

PLATE XXV. 



A — the floor on which the flails are 
fixed. 

B — the part of the floor on which the 
grain is laid, made of wicker-work, 
through which the grain falls, and is 
conveyed to the fan or screen below; 
the pivot of the fan is seen at P, and 
is turned by a band from the wheel, 
or wallower. 

C C C — a thin board raised round the 
floor to confine the wheat, and made 
shelving outwards, to render raking 
off the straw more easy. 

D — the wallower or wheel. 

E — Crank handle to turn the wheel. 

F F— Flails. 

G G G — Lifters, with ropes fixed to the 
flails. 



1 1 1 — Catchers or teeth to raise the lift- 
ers. 

K — Post on which. the wallower is fixed. 

L — Beam on which the lifters rest and 
are fixed by an iron rod passing 
through the lifters, and let into this 
beam. 

M — Check beam to stop the end of the 
lifters from rising. 

N — keeps in which the lifters work. 

— Beam in which the ends of the flails 
are mortised. 

Q — Fly-ends loaded with lead, not ne- 
cessary in a horse machine. 

R — Showing the lifters and keeps, how 
fixed. 



The machine, to be worked by two men, was made on a scale of a 12 feet flail, 
having a spring which required a power of 20 lbs. to raise it three feet high at the 
point : — A spring of this power, and raised three feet high, being found to get out 
wheat with great effect. 

* The flail thrashing machine has been superseded by that with cylindrical beat- 
ers and a concave, variously modified. This is now so generally introduced as 
not to require any description. The flail machine having been originally engraved 
for this work, has been retained. 



APPENDIX, 



CONTAINING 

A DESCRIPTION OF A MERCHANT FLOUR MILL, ON THE MOST 
APPROVED CONSTRUCTION, WITH THE RECENT IMPROVE- 
MENTS, WITH TWO ADDITIONAL PLATES. 

BY CADWALLADER AND OLIVER EVANS, ENGINEERS; 



EXTRACTS 

FROM SOME OP THE BEST MODERN WORKS ON THE SUBJECT OF MILLS, 
WITH OBSERVATIONS BY THE EDITOR. 



Description of a Merchant Flour Mill, driving four Pairs 
of five feet Mill-Stones ; arranged by Cadwallader and 
Oliver Evans, Engineers, Philadelphia. 

PLATE XXVII. 

1 — A hollow cast-iron shaft, circular, 15 inches in dia- 
meter except at those points where the water and main 
bevel wheels are hung, where it is increased to 19 
inches in diameter. The water-wheel is secured on 
this shaft by 3 sockets, as represented in Plate 
XXVIII., fig. 3, and makes 10 revolutions per minute. 

2 — The main driving bevel-wheel, on the water-wheel 
shaft, 8 feet in diameter, to the pitch line; 100 cogs, 
3 inches pitch, and 8 inches on the face, revolving 10 
times per minute, and driving 

3 — A bevel-wheel on the upright, 4 feet in diameter to 
pitch line; 50 cogs, same pitch and face of cogs as 
above, revolving 20 times per minute. 

4 — The large pit spur-wheel, making 20 revolutions per 
minute, 9 feet \ inch diameter, to pitch line; 114 cogs, 



366 APPENDIX. 

3 inches pitch, face 10 inches; this wheel gives mo- 
tion to 

5, 5, 5, 5 — Four pinions on the spindles of the mill-stones, 
18,1 inches in diameter to pitch line, 19 cogs same 
face and pitch. 

6, 6, 6, 6 — Iron uprights shafts, extending the height of 
the building, and coupled at each story. 

7, 7, 7, 7 — Are 4 pairs of five feet mill-stones, making 
120 revolutions per minute. Two of them shown in 
elevation; and the position of the 4, shown in Plate 
XXVIII. as represented by the dotted lines fig. 1. 

8 — A pulley on the upright shaft, which, by a band, gives 
motion to 

8 — The fan for cleaning grain, revolving 140 times per 
minute, wings 3 feet long, 20 inches in width. 

9 — A bevel wheel 2 feet diameter, cogs 2 inches pitch, 
face 2,5 inches, on the upright shaft, gearing into a 
bevel wheel, the face of which is shown, drives the 
bolting screen 18 revolutions per minute. 

10 — A bevel wheel on upright shaft, 56 cogs, 2 inches 
pitch, 2,5 inches face, gearing into 

10 — A bevel wheel on the shaft of the bolting reels, 31 
cogs, same pitch and face. 

10, 10 — Are two of four bolting reels shown, 18 feet 
long, 30 inches diameter, revolving 36 times per mi- 
nute. 

1 1 — A large pulley on the upright shaft, which, by a 
band, gives motion to the rubbing stones 11. 

12 — A bevel wheel, on the top of the upright shaft gear- 
ing into 

12 — A bevel wheel, on the horizontal shaft, at one end 
of which is 

13 — A bevel wheel, 1 foot diameter, gearing into a be- 
vel wheel 

14 — of 5 feet diameter, which reduces the motion of the 
hopper-boy down to 4 revolutions per minute, which 
sweeps a circle of 20 feet. 

15 — Meal elevator attending 4 pairs of stones. 

16 — Grain elevator. 

17 — Packing-room and press. 



APPENDIX. 367 



PLATE XXVIII. 

Figure 1, 

A bird's eye view of the mode of giving motion to 4 pairs 

of mill-stones. 
4 — The large pit spur-wheel, driving at equal distances 

on its periphery, the pinions. 
5, 5, 5, 5 — attached to the spindles of the mill-stones. 
7, 7, 7, 7 — Mill-stones 5 feet diameter, represented by 

dotted circles. 

Figure 2, 

An enlarged view of the couplings of the upright shaft. 
They are of cast iron, with their holes truly reamed, 
to receive the ends of the iron upright shafts. 

2 — The face of a coupling, divided into 6. equal parts, 
radiating from the centre : three of the parts project, 
and three are depressed, so that when two of them are 
coupled, the projections of one will fill the depressions 
in the other, as 1, the coupling connected. 

Figure 3, 

A cast-iron socket for the water-wheel ; it is a plate fths 
of an inch thick ; the eye for the shaft to pass through 
1± inch thick, and 12 inches deep: the sockets, for 
receiving the arms, are 14 inches long; and have pro- 
jections 5 inches deep: 3 3 3, &c, are the projections; 
the intermediate space, between the sockets, are cut 
out to lessen the weight of metal, but in such a man- 
ner as to preserve the strength. It requires three of 
these sockets for a large water-wheel; the arms for re- 
ceiving the buckets, are dressed to fit tightly in the 
sockets; and secured firmly by bolts, as 2 2. 

Figure 4, 

Is an arm for the water-wheel, as dressed; 1, the end to 
be bolted in the socket; 2, the end for screwing on the 
bucket. 
The advantages of this mode of constructing water- 



38 S APPENDIX. 

wheels, is, that the shaft is not weakened, by having mor- 
tises cut in to receive the a!rm: that it is not so liable to 
decay, and if an arm or bucket be destroyed by acci- 
dent, they can be dressed out, and the mill stopped, only 
while you unscrew the broken part, and replace it by a 
new one. 

Figure 5, 

An elevation of the flour press. 1, the barrel of flour; 
2, the funnel; 3 3, the driver; 4 5, the lever; 4 3, the 
connecting bars, fastened by a strong pin to each side 
of the lever, at 4, and to the driver at 3. 6, a strong 
bolt, passing through the floor, and keyed below the 
joist; there is a hole in the upper part of the bolt, to 
receive a pin which the lever works on, which, when 
brought down by the hand, moves the pin 4, in the 
dotted circle; the connecting bars drawing down the 
driver 3 3, pressing the flour into the barrel; and as 
it becomes harder packed, the power of the machine 
increases; as the pin 4 approaches the bolt 6, the un- 
der sliding part of the lever is drawn out, to increase 
its length; and is assisted in rising by a weight fastened 
to a line passing over pulleys. 

When the pin 4 is brought down within half an inch 
of the centre of the bolt 6, or plumb line, the power in- 
creases from 1 to 288; and with the aid of a simple wheel 
and axis, as 1 to 15, from 288 to 4320; or, if the wheel 
and axis be as 1 to 30, it will be increased to 4320; that 
is to say, one man will press as hard with this machine as 
8640 men could do with their natural strength. It is 
extremely well calculated for cotton, tobacco, cider, or, in 
short, any thing that requires a powerful press. 

Operation of the mill:- — The grain, after having been 
weighed, by drawing a slide, is let into the grain elevator 
16, then hoisted to the top of the building, and, by a 
spout moving on a circle, can be deposited into spouts 
leading to any part of the mill, when wanted for use: by 
drawing sliders in other spouts, converging to the grain 
elevator 16, it can be re-elevated, and thrown into the 
hopper of the rubbing stones 11 ; after passing through 
which it descends into the bolting screen 9, and when 



APPENDIX. 369 

screened, falls into the fan 8, is there cleaned, and from 
that descends into a very large hopper, over the centre of 
the four pairs of mill-stones, which are supplied regularly 
with grain. After being ground, the meal descends into 
a chest, is taken by the elevator 15, to the top of the 
building, there deposited under the hopper-boy, which 
spreads, cools, and collects it to the bolting reels, where 
the several qualities are separated, and the flour descends 
into the packing room 17, where it is packed in barrels. 

By this arrangement, we dispense with all conveyers, 
and have only one grain, and one flour elevator, to attend 
two pairs of stones; we also dispense with one-half the 
quantity of gearing usually put into mills, and conse- 
quently, occupy much less space, leaving the rest of the 
building for stowing grain, &c. 

All the wheels in this mill are of cast iron, and the face 
of the cogs very deep ; for experience justifies the asser- 
tion that depth of face in cog-wheels, when properly con- 
structed, does not increase friction; and that the wheels 
will last treble the time, by a small increase of depth: we 
recommend the main driving wheels to be 10 inches on 
the face. The journals of. all shafts, when great pressure 
is applied, should be of double the length now generally 
used; increase of length does not increase friction; say 
for water-wheels, journals of from 8 to 14 inches. 

CADWALLADER EVANS, 
OLIVER EVANS. 

June 15, 1826. 



24 



370 APPENDIX. 



WATER-WHEELS. 



On the Construction of Water-Wheels, and the method of 
applying the water for propelling them, so as to produce 
the greatest Effect. 

The following article is from the pen of a practical en- 
gineer of experience and talents ; his observations are, in 
general, in perfect accordance with those of the editor. 
The principles which he advocates are undoubtedly cor- 
rect, and it is hoped that their publication in this work 
will induce some of our most intelligent mill-wrights to 
forsake the beaten track, and to practise the modes re- 
commended. Let them recollect that Mr. Parkin was 
not a mere theorist, but a practical man, like themselves. 
The death of this gentleman has deprived society of the 
service of one of its members, from whose liberality, ex- 
perience, and skill, much was expected. 

[from the franklin journal.] 

In constructing water-wheels, especially those of great 
power, the introduction of iron is a most essential im- 
provement, and if this metal, and artisans skilled in work- 
ing it, could be obtained at reasonable rates, water-wheels 
might be made wholly of it, and would prove, ultimately, 
the cheapest; for if managed with due care, and worked 
with pure (not salt) water, they would last for centuries ; 
but, as the first cost would be an objection, I would re- 
commend, in all very large wheels, that the axis be made 
of cast-iron; and, in order to obtain the greatest strength 
with the least weight, the axis or shaft ought to be cast 
hollow, and in the hexagon or octagon form, with a strong 
iron flanch, to fix each set of arms, and the cog-wheel, 
upon ; these flanches to be firmly fixed in their places with 
steel keys. 

On the adaptation of water-wheels to the different 
heights of the water falls by which they are to be worked, 
I will remark that falls of from 2 to 9 feet, are most ad- 



APPENDIX. 371 

vantageously worked with the undershot wheel; falls of 
10 feet and upwards, by the bucket or breast-wheel, 
which, up to 20 or 25 feet, ought to be made about one-sixth 
higher than the fall of water by which it has to be worked ; 
and in wheels of both descriptions, the water ought to 
flow on the wheel from the surface of the dam. I am 
aware that this principle is at direct variance with the 
established practice, and perhaps there are few wheels in 
the States that can be worked, as they are now fixed, 
by thus applying the water; the reasons will be apparent 
from what follows. 

In adjusting the proportions of the internal wheels by 
which machinery is propelled, it is necessary, in order 
to obtain the greatest power, to limit the speed of the 
skirt of the water-wheel, so that it shall not be more than 
from 4 to 5 feet per second; it having been ascertained, 
by accurate experiments, that the greatest obtainable 
force of water, is within these limits. As a falling body, 
water descends at the speed of about 16 feet in the first 
second, and it will appear evident that if a water-wheel 
is required to be so driven, that the water with which 
it is loaded has to descend 10, 11, or 12 feet per second, 
at which rate wheels are generally constructed to work, 
a very large proportion of the power is lost, or, rather, is 
spent, in destroying, by unnecessary friction, the wheel 
upon which it is flowing. 

In the common way of constructing mill work, and of 
applying water to wheels, it has been found indispensa- 
bly necessary to have a head of from 2 to 4 feet above 
the aperture through which the water flows into the 
buckets, or against the floats of a water-wheel, in order 
to be able to load the wheel instantaneously, without 
which precaution, it could not be driven at the required 
speed ; from this circumstance it has been erroneously in- 
ferred, that the impulse or shock which a water-wheel, 
so filled receives, is greater than the power to be derived 
from the actual gravity of the water alone. This theory 
I have heard maintained among practical men; but it is, 
in (act, only resorting to one error to rectify another. 
Overshot wheels have been adopted, in numerous cases, 
merely for the purpose of getting the water more readi- 



372 APPENDIX. 

]y into the buckets; but confine the wheel to the proper 
working speed, and that difficulty will not exist. 

In consequence of the excessive speed at which wa- 
ter-wheels are generally driven, a small accumulation of 
back water either suspends or materially retards their 
operations; but, by properly confining their speed, the 
resistance from back water is considerably diminished,' 
and only amounts to about the same thing as working 
from a dam as many inches lower as the wheel is im- 
mersed; and in undershot wheels worked from a low head, 
or situated in the tide-way, the resistance from back wa- 
ter may be farther obviated by placing the floats not ex- 
actly in a line from the centre of the wheel, but deviating 
6 or 8 inches from it, so as to favour the water in leaving 
the ascending float. 

In constructing water-wheels to be driven at the speed 
of 4 or 5 feet per second, it will be requisite to make 
them broader, to work the same quantity of water which 
is required to drive a quick-speeded wheel. Thus, if a 
person intending to erect a mill, has a stream sufficient to 
work a wheel 5 feet broad, the skirt to move 10 feet per 
second, it is evident that if he wishes to work all the wa- 
ter which such wheel takes, he must have his wheel 10 
or 12 feet broad, instead of 5, otherwise the water must 
run to waste, as there would not be room, in a slow- 
moving wheel of 5 feet broad, to receive more than half 
of it. The principal advantages resulting from the pro- 
posed method of adapting wheels to the falls by which 
they are to be worked, and the method of applying wa- 
ter, are — 

1. The lessening of friction upon the main gudgeons, 
(and first pair of cog-wheels) by which, with a little care, 
they may be kept regularly cool, and the shaft or axis be 
preserved much longer in use than when the gudgeons 
cannot be kept cool. 

2. By working water upon the principle of its actual 
gravity alone, and applying it always at the height of the 
surface of the dam, its power is double what is obtained 
by the common method of applying it. 

3. The expensive penstock required to convey the 
water to the wheels, generally used, will not be needed, 



APPENDIX. 373 

as one much shallower, and consequently less expensive, 
will be sufficient. 

4. The resistance of back water h reduced as far as 
possible. 

5. The risk of fire is less, as the friction is reduced. 

W. Parkin, Engineer. 

September 24th, 1825. 



That water, whenever the fall is sufficient, ought always 
to be applied upon the principle of its actual gravity, ap- 
pears to be a conclusion so obvious, that it is astonishing 
it should ever be disputed. The acknowledged differ- 
ence between the effect of overshot and undershot wheels, 
is an evidence of the truth of the principle. The whole 
moving power of water is derived from its gravity : it is 
this which causes it to fall, and although in falling from 
a given height it acquires velocity, its gravitating force 
remains the same, and all the effect which this might 
have produced, has been expended upon itself, and not 
in moving any other body. The force with which water 
strikes, after it has fallen from any height, is calculated 
to deceive those who are not well grounded in the prin- 
ciples of hydrostatics; but it is admitted, both by Mr. 
Evans and Mr. Ellicott, that the effect upon overshot 
wheels is diminished by increasing the head, and the reason 
given for leaving the head so great as they prescribe, is 
the necessity of filling the buckets with sufficient rapi- 
dity ; this necessity, however, is created by giving too 
much velocity to the wheel. 

It has been stated by Mr. Evans, and is generally be- 
lieved by mill-wrights, that it is necessary to give a much 
greater velocity to wheels, than that which is recom- 
mended by Smeaton and others, in order to cause the 
mill to run steadily, and prevent its being suddenly 
checked by an increased resistance. This is saying that 
the water-wheel ought to be made to operate as a fly- 
wheel, which it will not do if its motion be slow. The 
objection to this is twofold. By giving to the skirt of 



374 APPENDIX. 

the wheel a motion much exceeding 4 or 5 feet per se- 
cond, its power is considerably reduced below the maxi- 
mum, and this loss of power is perpetual; wasting a con- 
siderable portion of water, to convert the water-wheel 
into a fly-wheel, which water might be employed in 
giving greater power to the mill. When a mill, from the 
nature of the work which it has to perform, requires the 
action of a fly-wheel, the situation of the water-wheel is 
often the worst that could be devised for this purpose, 
especially where there is any considerable gearing in the 
mill. A fly-wheel does not add actual power, but it 
serves to collect power, where the resistance is unequal | 
and in order to its producing this effect most perfectly, 
it ought to be placed as near as possible to the working 
part of the machinery. In grist mills there is no neces- 
sity for a fly-wheel; the stones perform this office in the 
most effectual manner, and the same remark is applica- 
ble to every kind of mill without a crank, and in which 
the resistance is equal, or nearly so, during the whole 
time of its action. 

Although we have spoken highly of the general views 
given by Mr. Parkin, in his communication to the Frank- 
lin Journal, he has fallen into some mistakes, which were 
pointed out by a writer in the same publication, Vol. IV., 
page 166. A part of this communication is subjoined, 
as it contains remarks, and a tabular view of the veloci- 
ties attained, and the distances fallen through, by bodies, 
in fractional parts of a second, which may be of great 
practical utility: — 

"I suppose that, at the present day, no man who pro- 
fesses to be capable of directing the construction of a water 
wheel, or of estimating the amount of a water power, 
gnorant of the fact, that water falls through a 
distance of about sixteen feet in the first second. But I 
suspect that many who assume the above qualifications, 
do not know the ratio of increase, either in the distance, 
or the velocity. I have drawn this conclusion, not only 
from conversations with several practical engineers, but, 
also, from essays published in our scientific journals. As 
an instance of the latter, I will select, for its convenience 



APPENDIX. 375 

of reference, an article on water-wheels, published in this 
Journal, (Vol. 1. p. 103,) which being the production of 
a practical engineer, and having passed the inspection of 
a scientific committee, may be considered as corroborating 
my commencing observations. In the third paragraph of 
that article is the following sentence: 'As a falling body, 
water descends at the speed of nearly 16 feet in the first 
second, and it will appear evident, that if a water-wheel 
is required to be so driven, that the water with which it 
is loaded has to descend 10, 11, or 12 feet per second, at 
which rates wheels are generally constructed to work, 
that a very large proportion of the power is lost.' 

" Here, in the first place, we find speed, or velocity, con- 
founded with the distance fallen in the first second; 
whereas, the latter is 16 feet, and the former is accele- 
rated, from nothing, at the commencement, to 32 feet per 
second, at the end of the first second ; so that this part of 
the sentence conveys, strictly, no intelligible meaning; it 
is, nevertheless, made a standard, by a comparison be- 
tween which, and any given velocity of a water wheel, 
we are to infer the loss of power sustained through ex- 
cess of speed; thus, in the ease of a wheel whose velocity 
is 10 or 12 feet per second, comparing these numbers 
with the mysterised number 16, the writer concludes, 
' that a very large proportion of the power is lost.' The 
height of the fall which indicates the whole amount of 
the power, is not mentioned, but surely, to estimate the 
proportion between a defined part, and undefined whole, 
is impossible. 



"I have made a calculation of the distances and velo- 
cities attained by falling bodies, in various fractional 
parts of a second, which is here introduced for the infor- 
mation of those practical and theoretical engineers who 
have avoided the labour of doing it for themselves. 

"I have proceeded on the following established data, 
namely : 

"Heavy bodies fall through a distance of 16 feet, in 
the first second; at the end of which they have acquired 



376 



APPENDIX. 



a velocity of 32 feet per second. — The velocity increases 
as the times. — The distance increases as the square 
of the times. 



Time of Descent. 


Distance fallen. 


Velocity attained 
per second. 


i IS; 


feet. 


inches. 


feet, inches. 


M '*"• • 





<V«r 


3 


2 . . 





<Vt 


6 


3 . . 





°A 


9 


4 )■ 128ths of a sec. 





°A 


1 


5 


. 





Of 


1 3 


6 


. 





Of 


1 6 


7 







n 


1 9 


2 ; 


• 





n 


2 


3 







1* 

*~5 


3 


4 
5 


>32ndsof a sec. 


0' 



3 

4! 


4 
5 


6 


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"To determine what proportion of a given water 
power is lost by a given velocity of the wheel, it is only 



APPENDIX. 377 

necessary to ascertain what distance the water must de- 
scend to acquire that velocity. Then this distance, com- 
pared with the whole fall, answers the question. Thus : 
suppose the whole fall to be 10 feet, and the velocity of 
the wheel 4 feet per second ; this velocity is due to a fall 
of 3 inches, or one-fortieth part of the whole fall, which 
is the proportion sought. Or, suppose the velocity to be 
13 feet per second, which is due to a fall of 2 feet 7| 
inches, then the loss is rather more than one-fourth of 
the whole fall of 10 feet. But it must be especially 
noted, that these estimates embrace the supposition, that 
the water issues upon the wheel in the direction of the 
motion of its skirt, and precisely at that distance below 
the surface of the dam, which answers to the velocity of 
the wheel. Inattention to this particular, is a very im- 
portant and frequent cause of loss. L. M." 

With respect to the actual advantage of giving to over- 
shot wheels a motion much less rapid than that usually 
given, the following example will probably have more 
effect on the mind of the mere practical workman, than 
any reasoning that could be offered : and, in fact, reason- 
ing would be of little value, were it not supported by 
practical results. 

The subjoined account is from the Technical Reposi- 
tory, a work published in London : — 



" On the comparative Advantages of different Water Wheels, 
erected in the United States of America, by Jacob Per- 
kins, Esq. ; and in this Country, by Mr. George Man- 
waring, Engineer. 

"Mr. Perkins erected at NeAvburyport, a water 
wheel of 30 feet in diameter, on the plan of what is termed, 
in America, a pitch-back; but, in this country, a back- 
shut; that is, one which receives the water near to its 
top, but not upon it, as in over shot-wheels ; this is, in- 
deed, the most judicious mode of laying water upon the 
wheel; as, in case of floods, the wheel moves in the same 
direction with the water, and not in the opposite one ; 
neither is it encumbered, as in the overshot wheel, with 



378 APPENDIX. 

a useless load of water at its top, where it does nothing 
but add to the weight upon the necks or pivots of the 
wheel-shaft, and to the consequent loss of power by the 
increased friction upon them ; whereas, in the pitch-back, 
or bach-shut wheel, the water is laid on at a point, where 
it acts by its leverage in impelling the wheel, and has 
yet time to become settled in the buckets, previously to 
its reaching the point level with the axis, where it acts 
with its greatest power. The wheel itself was construct- 
ed of oak; but with iron buckets; and it had a ring of 
teeth around it, which drove a cast-iron pinion, of three 
feet in diameter, which gave motion to three lying shafts, 
each of thirty feet in length, coupled together, so as to 
form a line of ninety feet; and from which, the necessary 
movements were communicated to the machinery for 
making nails. 

"Mr. Perkins placed his pinion as close as possible un- 
der the pen-trough, which delivered the water upon the 
wheel ; and he thus greatly lessened the weight upon the 
necks or gudgeons of the wheel-shaft, by suspending it, 
as it were, upon the pinion; whereas, had he, as is usual, 
placed it on a horizontal line with the axis of the wheel, 
and on the opposite side of it, he would have loaded the 
necks with a double weight; namely, the water upon one 
side of the wheel, and the resistance opposed by the ma- 
chinery to be driven by it, on the other. He also took 
care that the teeth upon the wheel, and the pinion 
should always be kept wet, or run in water, instead of 
being greased, as is usual, and this he found sufficient to 
cause them to run smoothly and without the least noise. 
The motion of the wheel's periphery was about three 
feet per second, agreeably to the improved theory, so 
ably demonstrated by the late scientific Mr. Smeaton ; 
and it continued to perform its work, with great satisfac- 
tion to its owners, for ten years, when it was unfortunate- 
ly destroyed by fire. 

"An opportunity soon presented itself of comparing 
the advantages of this water-wheel with another, which 
the proprietors were induced to erect on the representa- 
tions of a mill-wright, that the wheel was too high, and 
that it would be much better, were it only twenty-three 
feet in diameter, and received its water at the breast. 



APPENDIX. 379 

The trial, however, proved, that in driving the nail ma- 
chinery, which had escaped the fire that destroyed the 
water-wheel, the new wheel required twice the quantity of 
water to work it which actuated the former one, and only 
did the same work. 

"Mr, Man waring has also had an opportunity of veri- 
fying, in this country, the advantages of a construction 
similar to Mr. Perkins's, in a cast-iron back-shut water- 
wheel of the same diameter as his, (namely, thirty feet,) 
and which also has a ring of teeth around it, driving a 
pinion of three feet in diameter, posited of the same side 
of the wheel as Mr. Perkins's, but not quite so high, it 
being a little above the centre of the wheel, and the teeth 
of the wheel and pinion are always kept wet. This wheel 
is employed in grinding flour, at a corn-mill in Sussex, 
and drives six pairs of stones, besides the other necessary 
machinery, it moving at the rate of about three feet per 
second; and so great satisfaction has it given, that Mr. 
Manwaring is now constructing another water-wheel 
upon the same plan, and for the same proprietor; only 
that it will be wider, and is calculated to drive eight 
pairs of stones. 

"We are glad to have this opportunity of communi- 
cating these valuable practical facts: the same results be- 
ing also obtained in two countries so widely separated as 
the United States and England, make them more valua- 
ble; and prove, that when persons think rightly, they 
will naturally think alike." 



The foregoing example, although it relates to a pitch- 
hack wheel, may serve our purpose as well as if it had 
been an overshot; there being an evident similarity be- 
tween an overshot, with the water delivered on the top, 
with but little head, and the pitch-back, as constructed 
by Mr. Perkins; and also, between an overshot with con- 
siderable head, and the breast wheel. 

The remarks made upon pitch-back wheels, are wor- 
thy the serious attention of the mill-wright. Mr. Evans 
very correctly compares them, in their action, to over- 



330 APPENDIX. 

shots: Mr. Ellicott thinks "an overshot with equal 
head and fall, is fully equal in power," and has dismissed 
them in a very few words. The reason of this is evident; 
the head, which they thought to be necessary, was not 
so easily managed with the pitch-back, as with the over- 
shot; but when it is admitted, that the water should be 
delivered at the surface of the dam, that the velocity of 
the wheel should not exceed 4 or 5 feet per second, and 
that its capacity for containing water should be increased, 
the difficulty vanishes altogether. The water, when 
emptied from the buckets, has its impulse in the right, 
direction to carry it down the tail-race; and in case of 
back water, the greater facility with which it will move 
is undeniable. , 

With respect to undershot wheels, Mr. Evans con- 
cludes that they ought to move with a velocity nearly 
equal to two-thirds of that of the water, and Mr. Ellicott 
estimates the velocity at quite two-thirds. It would be 
saying but little to assert that this did not agree with 
theory; but it does not accord with the opinions of many 
intelligent and experienced mill-wrights. It was as- 
serted, upon theory, that the power of an undershot 
wheel would be at a maximum, when the velocity of the 
floats of the wheel was equal to one-third of the velocity 
of the water; practice, however, did not confirm the 
truth of this theory; and Borda has shown that the con- 
clusion was theoretically incorrect, applying only to the 
supposition that the water impelled a single float-board; 
but that in the action upon a number of float-boards, as 
in a mill-wheel, the velocity of the wheel will be one-half 
the velocitv of the water, when the effect is a maximum. 
The demonstration of this may be seen under the article 
Hydrodynamics, in the Edinburgh Encyclopedia. This 
was fully confirmed by the experiments of Smeaton, who, 
in speaking upon them, observes, that "in all the cases 
in which most work is performed in proportion to the 
water expended, and which approach the nearest to the 
circumstances of great works, when properly executed, 
the maximum lies much nearer to one-half, than one-third, 
one-half seeming to be the true maximum." 



APPENDIX. 3S1 

The succeeding observations are extracted from " Prac- 
tical Essays on Mill-work and other Machinery, by 
Robertson Buchanan." Cast iron is very generally em- 
ployed in England, not only for the wheel-work of mills, 
but, also, for many parts of the framing ; the same prac- 
tice obtains in those parts of our own country where 
castings can be procured with facility, and will gain 
ground as its real value becomes known. Of course, the 
following extracts apply, in many instances, to the use of 
this material; but it will be found that the principles 
upon which they are founded, will in general apply to 
wood as well as to iron. 

il A Practical Inquiry respecting the Strength and Durability 
of the Teeth of Wheels used in Mill-work, 

" Having treated of the forms of the teeth of wheels, I 
come now to consider their proportional strength, with 
relation to the resistance they have to overcome. 

"I am aware, that owing to a great variety of circum- 
stances, this subject is involved in much difficulty, and 
that it is no easy task to form any general rule with re- 
gard to the pitches and breadths of the teeth of wheels. 
I do not pretend to more than a mere approximation 
towards general rules; yet, were this judiciously done, I 
am of opinion that it might be useful to the mill-wright, 
who has not had leisure or opportunity for scientific in- 
quiries. A rule, though not absolutely perfect, is better 
in all cases than to have no guide whatever. 

" And it is too evident to require proof, that it is essen- 
tial to the beauty and utility of any machine, that the 
strength and bulk of its several parts be duly propor- 
tioned to the stress, or wear, to which the parts may be 
subject. 

"Some general observations on the wheel-work of 
mills, will serve greatly to simplify our inquiries on the 
subject. 



382 APPENDIX. 



" General Observations on the Wheel-work of Mills. 

"Mistaken attempts at economy have often prompted 
the use of wheels of too small diameter. This is an evil 
which ought carefully to be avoided. Knowing the pres- 
sure on the teeth, we cannot, with propriety, reduce the 
diameter of the wheel below a certain measure. 

"Suppose, for instance, a water-wheel of 20 horses' 
power, moving at the pitch line with a velocity of 3| feet 
per second. It is known that a pinion of 4 feet diameter 
might work into it, without impropriety ; but we also 
know that it would be exceedingly improper to substitute 
a pinion of only one foot diameter, although the pressure 
and velocity at the pitch lines, in both cases, would be in 
a certain sense, the same. In the case of the small pinion, 
however, a much greater stress would be thrown on the 
journeys (or journals) of the shaft. Not, indeed, on ac- 
count of tortion or twist, but on account of transverse 
strain arising as well from greater direct pressure, as 
from the tendency which the oblique action of the teeth, 
particularly when somewhat worn, would have to produce 
great friction, and to force the pinion from the wheel, and 
make it bear harder on the journals. The small pinion 
is also evidently liable to wear much faster, on account of 
the more frequent recurrence of the friction of each par- 
ticular tooth. 

"That these observations are not without foundation, 
is known to mill-wrights of experience. They have 
found a great saving of power by altering corn mills, for 
example, from the old plan of using only one wheel and 
pinion, (or trundle,') to the method of bringing up the 
motion by means of more wheels and pinions, and of 
larger diameters and finer pitches. 

"The increase of power has often, by these means, 
been nearly doubled, while the tear and wear has been 
much lessened; although it is evident, the machinery, 
thus altered, was more complex. 

"The due consideration of the proper communication 
of the original power, is of great importance for the con- 
struction of mills, on the best principles. It may easily 



APPENDIX. 383 

be seen that, in many cases, a very great portion of the 
original power is expended, before any force is actually 
applied to the work intended to be performed. 

"Notwithstanding the modern improvements in this 
department, there is still much to be done. In the usual 
modes of constructing mills, due attention is seldom given 
to scientific principles. It is certain, however, that, were 
these principles better attended to, much power, that is 
unnecessarily expended, would be saved. In general, 
this might be in a great measure obtained by bringing 
on the desired motions in a gradual manner, beginning 
with the first very slow, and gradually bringing up the 
desired motions by wheels and pinions of larger diame- 
ters. This is a subject which should be well considered, 
before we can determine, in any particular case, what 
ought to be the pitch of the wheels. In the case above 
alluded to, where the supposition is a pinion of 4 feet 
diameter, or of 1 foot diameter, it is obvious, that the same 
pitch for both would not be prudent: that for the small 
pinion, ought to be much less than that which might be 
allowed in the case of the larger pinion. It is also equally 
obvious, that the breadth of the teeth, in the case of the 
small pinion, ought to be much greater than that in the 
case of the larger pinion. 

" It is evident, however, that although great advantage 
may often be derived from a fine pitch, that there is a 
limit in this respect, as also with regard to the breadth. 
We shall endeavour to find some trace of this limit in 
what follows: and, that we may the better do this, we 
shall call in the aid of propositions, which are true with 
respect to pieces of timber, or metal, subjected to ordinary 
causes of pressure. It is allowed that they cannot here, 
in strictness, be demonstrated, as applicable to wheel- 
work. Yet they will, for want of better light, serve at 
least to prevent any material practical error, with regard 
to the strength of the teeth of the wheels. For it is to be 
remembered, that we are not so much here in search of 
truths of curious or profound mathematical speculation, 
as of that kind of evidence of which the subject admits, 
and which may be sufficiently satisfactory for any prac- 
tical purpose. 



384 APPENDIX. 

"As cast iron pinions are now generally used, and as 
the teeth of the pinion are most subject to wear, I think 
we are safe in the present inquiry, in considering them 
all as cast iron. 

" The laws to which I have alluded in this investiga- 
tion, are these: — 

" ' Principles of proportioning the Strength of Teeth of 

Wheels. 

"'PROPOSITION I. 

" ' The strength of any Piece of Timber or Metal, whose 
section is a Rectangle, is in direct Proportion to the breadth, 
and as the Square of the Depth. 9 * 

" Hence, may be inferred, that the strength of the teeth 
of wheels, moving at the same velocity, and under the 
same circumstances, is directly in proportion to their 
breadth, and as the square of their thickness. Thus, for 
example, if we double the breadth, we only double the 
strength ; but if we double the thickness, or, in other 
words, double the pitch, keeping the original breadth, we 
increase the strength four times. 

" For although when wheels are working accurately, 
the strain is, at the same time, divided over several teeth ; 
yet as a very small inaccuracy, or even the interposition 
of any small body, such as a chip of wood, or stone, throws 
the whole stress upon a single tooth, in practice ; there- 
fore, and in order to simplify this case, we may consider 
the strength of a single tooth as resisting the pressure of 
the whole work. 

" But as the length of the teeth commonly varies with 
the pitch, this circumstance must be taken into account, 
and the most simple view we can take of it seems to be 
that of having the strain of each tooth thrown all to the 
outward extremity: we have then the following proposi- 
tion to guide this part of our inquiry: — 

PROPOSITION II. 

"' If any Force be applied laterally to a Lever or Beam, 

* See Emerson, Prop. 67. 



APPENDIX. 385 

the Stress upon any plate is directly as the Force and its 
distance from that plated* 

" ' PROPOSITION III. 

" ' The pitch being the same, the Stress is inversely as 
the Velocity." 1 ^ 

" For example — if the pitch lines of one pair of wheels 
be moving at the rate of 6 feet in a second, and another 
pair of wheels, in every other respect under the same cir- 
cumstances, be moving at the rate of 3 feet in a second, 
the stress on the latter is double of that on the former. 



" Of arranging the Numbers of Wheel- Work, 

" In a machine, the velocity of the impelled point 
should be to that of the working point, in the ratio which 
is adapted to the maximum effect of the moving power 
oft the one part, and the best working effect on the other 
part. Any other arrangement of the relative motions of 
the parts of a machine must clearly be attended with a 
loss of power, or the work will not be done properly. 
But when the best working velocity is known, and, also, 
that which enables the first mover to produce the great- 
est effect, the proper arrangement of the numbers of the 
teeth of the wheels and pinions is a very simple opera- 
tion. 

"It will be an advantage to advertise the young me- 
chanic of one or two essential particulars, before proceed- 
ing to the principal object. 

"In the first place when the wheels drive the pinions, 
the number of teeth in any one pinion should not be less 
than 8; but rather let there be 11 or 12, if it can be done 
conveniently. And in the particular form of teeth pre- 
viously described, the number of teeth in a pinion should 
not be less than 10; but it would be better to have 13 
or 14. 

"Secondly — When the pinions drive the wheels, the 
number of teeth on a pinion may be less; but it will not, 

* See Emerson, Prop. 69. f See Emerson, Prop. 119, Rale 8. 

25 



386 APPENDIX. 

in any case, be desirable to have fewer than 6 teeth on a 
pinion; and give the preference to 8 or 9, where it can 
be done with convenience. 

"Thirdly — The number of teeth in a wheel should be 
prime to the number of teeth in its pinion, that is, the 
number representing the teeth in the wheel should not 
be divisible by the number of teeth in the pinion without 
a remainder. And as the numbers of pinions will, in 
general, be first settled, it will be an advantage to take 
a prime number for each pinion, as 7, 11, 13, 17, 19, 
23, &c, because such numbers are more seldom factors 
than others. But when it happens that a prime number 
can be directly fixed upon for the wheel, any whole num- 
ber which approaches near to the required ratio will an- 
swer for the pinion; as minute accuracy is not required. 
A prime number for the wheel, or one which is not di- 
visible by the number of the pinion, is esteemed the best, 
because the same teeth will not always come together, 
and the wear will be more uniform. * 

"Fourthly — If it be desired that a given increase or 
decrease of velocity should be communicated, with the 
least quantity of wheel-work, it has been shown that the 
number of teeth on each pinion should be to the number 
on its wheel, as 1 : 3,59 (Dr. Young's Nat. Phil. Vol. II. 
Art. 366.) But, on account of the space required for 
several weeks, and the expense of them, it will often be 
necessary to have 5 or 6 times the number of teeth on 
the wheel that there is on the pinion. The ratio of 1 : 6 
should, however, not be exceeded, unless there be some 
other important reason for a higher ratio." 



" Practical Observations with regard to the making of Pat- 
terns of Cast Iron Wheels. 

"Having determined the pitch of the wheel strong 
enough for the purpose to which it is to be applied, the 
thickness of the tooth serves to regulate the proportionate 
strength of the other parts. 



APPENDIX. 387 

"A very respectable mill-wright informs me, that he 
has for a considerable time adopted the following rule 
for determining the length of the teeth of wheels, the 
practical efficacy of which he has found quite satisfac- 
tory:— 

"Rule — Make the length of the teeth equal to the pitch, 
deducting freedom, (by the freedom is meant the distance 
at the top of one tooth and the root of another, measured 
at the line of centres,) in other words, the distance from 
root to root of the teeth, at the line of teeth, when the 
wheels are in action, exactly equal to the pitch. 

" For example — he makes the teeth of two inches pitch, 
one inch and thirteen-sixteenths in length, which is allow- 
ing three-sixteenths of freedom. 

"Another respectable mill-wright, who has had much 
experience, particularly in mills moved by horses, has, 
for a considerable time past, made the teeth of his wheels 
only one-half of the pitch in length, and works them as 
deep as possible, without the point touching the bottoms. 
Before he fell on this expedient, he found the teeth ex- 
ceedingly liable to be broken from any sudden motion of 
the horses. 

"Indeed, upon reflection, it will be found that there is 
no occasion for more freedom than that the point of the 
tooth of the one wheel shall just clear the ring of the 
other; more than this must only serve to weaken the 
teeth. The mode of gearing, however, above alluded to, 
is more necessary in horse mills than where the moving 
power is steady and regular. 

" Hutton (on clock-work) recommends making the dis- 
tance of the pitch line three-fourths of what we call the 
thickness of the tooth. Thus, suppose the rule applied 
to a two inch pitch, and that the tooth and space were 
exactly equal, then the tooth would project three-fourths 
of an inch beyond the pitch line, and its root would be as 
far within the pitch line, as to receive freely the tooth in- 
tended to act on it; suppose it also three-fourths, then the 
tooth would be one and a half inch long, besides the free- 
dom, which making, as above, three-sixteenths, the tooth 
would be in all one and eleven-sixteenths inch long. 



388 APPENDIX. 

"But it is to be remarked, that the mill-wright, in 
making his pattern for a cast iron wheel, has to attend to 
a circumstance arising from the nature of that material. 
The pattern must not only be of such a form as to be suf- 
ficiently strong, calculating by the bulk of the parts, but 
also proportioned, so that when the fluid metal is poured 
in the mould, it may cool in every part nearly at the 
same time. 

" When due attention is not paid to this circumstance, 
as the metal is cooling, if it contract faster in one part 
than in another, it will be apt to break somewhere, just 
as a drinking glass is broken by suddenly cooling or 
heating in any particular part of it. In all patterns for 
cast iron, about one-eighth of an inch to the foot should 
be allowed for the contraction of the metal in cooling. 

"Attention must also be paid to taper the several parts 
so that they may rise freely without injuring the mould, 
when the founder is drawing them out of the sand. A 
little observation of the operations of a common foundry, 
will better instruct in this part of the subject than many 
words. We may observe, however, that about one-six- 
teenth of an inch, in a depth of 6 inches, is commonly a 
sufficient taper. 

"Attending to those circumstances, I beg leave to offer 
the following proportions as having been found to answer 
in practice. 

" Make the thickness of the ring equal to the thickness 
of the tooth near its root. When the ring is made thin- 
ner than the root of the tooth, the ring commonly gives 
way to a strain, which would not break the tooth. 

" Make the arm, at the part where it proceeds from the 
ring, of the same breadth and thickness as the ring, and, 
at the junction, let it be so formed as to take off any acute 
angle which would be apt to break off in the sand. 

"The arms should become larger as they approach the 
centre of the wheel, (see Emerson, Prop. 119, Rule 8,) 
and the eye should be sufficiently strong to resist the 
driving of the wedges, by means of which it is to be fixed 
on the shaft. This cannot be brought easily to calcula- 
tion. 



APPENDIX. 389 

" On the other hand, care must be taken not to make 
the eye so thick as to endanger unequal cooling. 

"It should be somewhat broader than the breadth of 
the teeth, in order that it may be the firmer on the shaft : 
this breadth must be greater in proportion as the wheel 
is large. 

" When the ring is about an inch thick, it is common 
to make the eye about an inch and a quarter in thickness, 
and about one-fifth broader than the ring, when the wheel 
is about four feet in diameter. 

" Small wheels have generally but four arms, but it 
being improper to have a great space of the ring unsup- 
ported, the number of arms should be increased in large 
wheels. 

"In order to strengthen the arms with little increase 
of metal, it is not unusual to make them feathered, which 
is done by adding a thin plate to the metal at right angles 
to the arm. 

"The same rules apply to bevelled wheels; of the 
practical mode of laying down the working drawings of 
which we have already spoken. But it is proper to ob- 
serve that the eye of a bevelled wheel should be placed 
more on that side which is farthest from the centre of the 
ideal cone, of which the wheel forms a part. 

"When wheels are beyond a certain size, it becomes 
necessary to have patterns sometimes made for them, 
cast in parts, which are afterwards united by means of 
bolts. 

"A very good mode to prevent the bad effects of une- 
qual contraction, is to have the arms curved; the curved 
parts are commonly of the same radius as the wheel, and 
spring from the half length of the arms." 



" Of Malleable or Wrought Iron Gudgeons." 

"Professor Robinson states,* that the cohesive force of 
a square inch of cast iron is from 40,000 to 60,000 lbs., 
wrought iron from 60,000 to 90,000 lbs. 

"In the year 1795, I had occasion to substitute cast 

* Encyclopaedia Britannica, article. Strength of Materials, 40. 



390 APPENDIX. 

iron gudgeons for those of wrought iron, and made some 
experiments on those metals, from which I drew the fol- 
lowing inference: that gudgeons of the same size, of cast 
and of wrought iron, in practice, are capable, at a medium, 
of sustaining weights without flexure in the proportion of 
9 to 14. 

"Taking it for granted that this proportion is near the 
truth, we may find the diameter which any wrought iron 
gudgeon ought to have when its lateral pressure is given, 
in the following manner: — 

"1. Find the diameter which a cast iron gudgeon 
should have to sustain the given pressure; then say, as 
14 is to the cube of the diameter of the cast iron gudgeon, 
so is 9 to the cube of the dia,meter of the wrought iron 
gudgeon. 

" 2. The root of this last number gives the diameter 
required of the wrought iron gudgeon. 

EXAMPLE. 
"Suppose the lateral pressure to be 125 hundred 
weights, the cube root of which is 5, the diameter in 
inches of the cast iron gudgeon : then say, 

As 14 

Is to .... 125 

So is ... . 9 

To . • . . 80,357 

"The cube root of which is 4,30887." 



" Of the Bearing of Shafts. 

" The bearings on which gudgeons and journals rest 
and revolve, are sometimes termed Pillows, and fre- 
quently Brasses, from being often made of that sub- 
stance. 

" It has become general to fix pillows in blocks of cast 
iron. Hence, the term Pillow Block, and sometimes, cor- 
ruptly, Plumber Block. 

"At the cotton works of Deanston, near Down, a water- 
wheel has run nearly 30 years on pillows of cast iron, 
with little sensible wear on the gudgeons, nor were they 
ever found liable to heat. 



APPENDIX. 391 

"The outer skin of cast iron, particularly when cast 
in metallic moulds, is remarkably hard, and it is reasona- 
ble to suppose that it would make a durable pillow, as 
we have seen is the case in the above instance." 



" On the Framing of Mill-Work. 

" Mill-work, from its motion, occasions a tremor on all 
the parts of its framing, which subjects it to much more 
speedy decay than the mere pressure upon carpentry. 

" Besides this general tremor, it is often subjected to 
violent, sudden thrusts, from the bad actions of the wheels, 
or from reciprocating motions. 

" It ought, therefore, to be not only sufficiently strong 
and stiff, but sufficiently heavtj, to give solidity and stea- 
diness, 

" Where the framing of the machinery is not firm and 
well bound, a vibratory motion in its parts, of course, 
takes place; which vibratory motion expends a conside- 
rable portion of the power applied. This loss of power 
is very difficult of investigation. It is certain, however, 
that whatever motion of a vibratory nature is communi- 
cated to the framing and objects in contact with it, (ab- 
stracted from the elasticity of the parts,) must be lost to 
the effect the machine would produce, were the parts 
sufficiently strong and well bound together; and it is to 
be observed, that firm and well bound framing is much 
preferable to heavy framing, not so well connected in its 
parts. It is as certain, that though the framing in either 
case may be constructed so as to be equally strong, yet 
the heavy framing, from its vibration, will expend more 
of the original power than that which is less heavy, but 
firmly connected. 

"Besides strength, stiffness, and solidity, the framing of 
mill-work requires to be constructed so as to be easy of 
repair ; and so contrived, that any particular part may be 
repaired or renewed with the least possible derangement 
to the other parts of the framing. 



392 APPENDIX. 

"There is another circumstance in this species of 
framing which demands great attention. The shafts often 
require to be restored to their true situations, from which 
they may have deviated by the wearing of the parts. 
Now the framing ought to be so constructed as easily to 
admit of this restoration of the shafts, as also of any other 
shifting of them which may in practice become neces- 
sary. : 

"But though the framing which supports the parts of 
mills and machines should be firm, it is an advantage 
that the part on which any axis rests should have a small 
degree of elastic tremor, when the machine is in motion. 
Such tremor has considerable power in diminishing the 
friction. It may farther be .observed, that framing to 
support machinery should be as independent of the build- 
ing as possible, because the tremor it always communi- 
cates is exceedingly injurious. 



On Reaction Wheels. 

Xhese wheels were slightly noticed at page 176; and 
a description of Barker's mill is to be found in nearly 
every work upon hydraulics, together with the improve- 
ment made in it by Rumsey. Within a few years past, 
wheels which operate upon the principle of the rotary 
trunk, in Barker's mill, have been extensively brought 
into use. We are not informed by whom they were 
invented; Mr. Evans alludes to them in the first edition 
of this work, published in 1795; but it does not appear 
certain that he had then seen them; it is manifest, 
at all events, that they were not publicly known. His 
words are, "One of these is said to do well where 
there is much back water; it being small, and of a true 
circular form, the water does not resist it much. I shall 
say but little of these, supposing the proprietors mean to 
treat of them." 

Their great merit, certainly, is their simplicity; and 
where there is a plentiful supply of water, they may, in 
many cases, be preferable to any other. Those interest- 



APPENDIX. 393 

ed in them aver that they are but little, if at all, inferior 
in economy to overshot mills; this, however, we are by 
no means prepared to admit. In back water they will 
undoubtedly operate better than any other, as there will 
not be any sensible loss from their wading, but only from 
the diminution of the effective head. In an eight feet 
fall, for example, should there be four feet of back water, 
the remaining four feet will produce nearly, or quite, its 
full effect. 

Many patents have been obtained for modifications of, 
and variations in, this wheel; and from the specification 
of one of them, as published in the journal of the Frank- 
lin Institute at Philadelphia, we will give such extracts 
as will suffice to exhibit their nature and mode of action. 
In doing this, we shall omit the claims of the patentee, 
as this is a point with which w 7 e, in this place, have no- 
thing to do. 

"Fig. 1, a bird's eye view of the wheel, Figure 1. 
the end to which the shaft is to be at- 
tached, at the perforation A, being down- 



wards, and the open end, or rim, upwards, :!(' c f^~^ ] \V: 
To show the floats, at the upper rim, which \a \S^J° j ); 
covers them, is not represented. The M^ D J } 
lines CC exhibit the form of the floats, or 2lZ^ y 
buckets, and the manner in which they are arranged. 
The diameter of this wheel, and the width of the floats 
between the two heads, and the depth of aperture be- 
tween the floats, will, of course, be varied according to 
the quantity and head of water which can be obtained, 
and the purpose to which it is to be applied. The 
curved floats, it will be seen, are made to lap over each 
other; and, in practice, it has been found that the pro- 
portion in which they do so is a point of considerable 
importance. The proportion between the aperture and 
lap which was found to be the best, is as three to two; 
that is, for every inch of aperture, measuring from float 
to float, at the point where the water escapes, the floats 
should pass each other one and a half inch. It will be 
manifest that a slight deviation from this proportion, in 
either way, will not be attended by any sensible loss of 
power. Any considerable deviation, however, is found 



394 



APPENDIX. 



to be injurious. The mechanic should be careful so to 
construct his wheel that the part of the aperture seen at 
e should be less than that seen at d. 

" Upon the inner edge of the rim there is a projecting 
fillet, or flanch, which may be seen in the section D, of 
this wheel, at the lower part of Fig. 3, with this differ- 
that said fillets or flanches are to be made flat as 




ence, 

they are to work against, and not within, each other. 

" Wheels so constructed may be applied either on a ho- 
rizontal or vertical shaft, and either singly or in pairs, ac- 
cording to circumstances. 

" Fig. 2 represents the Figim 

double reacting wheel, 
placed on a horizontal 
shaft, in which manner 
they are to be used, when- 
ever it is desirable to ob- 
tain motion from such a 
shaft. S is the horizontal 
shaft, A the penstock, and 
B the cistern; the heads 
or sides of the cistern, are 
formed in whole, or in 
part, of cast-iron plates, 
securely bolted together. D D are two water-wheels 
one of which is placed on each side of the cistern B, their 
open ends standing against the side plates of the cistern, 
which are perforated, having openings in them equal in 
size to those on the heads of the wheels, and being con- 
centric with them. The fillet, or flanch, upon the rim 
of each wheel, is made flat, and is fitted to run as closely 
to a similar fillet or flanch on the cistern head as may be, 
without actually bearing against it, so as to prevent too 
much waste of water, and yet to avoid friction by touch- 
ing it. 

The size of the orifices in the wheel and cistern plates 
is a point of essential importance, and should greatly 
exceed what has been heretofore thought necessary. 
Their area should be such as to permit the whole column 
of water to act unobstructedly on the wheel, whatever 
may be the height of the head. It is found that for a 



APPENDIX. 395 

head of four feet, the area of the orifice should never be 
permitted to fall short of three times the number of square 
inches which can be delivered by all the openings of the 
floats. The penstock, or gate-way, should also be suffi- 
ciently large to admit freely the same proportionate quan- 
tity of water through every part of its section ; say about 
three times the area of the orifices of the cistern heads 
and wheels. 

"For a greater head these openings must be propor- 
tionally increased, or the whole intention will be defeat- 
ed, as it has been from want of attention to this principle 
that numerous failures have occurred in the attempt to 
drive mills by reaction wheels. Whenever it is practica- 
ble, the limit which has been given should be exceeded, 
but never can be diminished without loss. 

"Instead of using a trunk or penstock, smaller than 
the horizontal section of the cistern B, extend the sides, 
front and back of said cistern, upwards in one continued 
line, whenever the same can be done; the cistern and 
penstock then form one trunk, of equal section through- 
out. 

" When greater power is requisite, place other react- 
ing wheels, or pairs of wheels, upon the same shaft, so 
that each may operate in the same way. 

"Fig. 3 represents one of the reacting Figure 3. 
wheels placed upon a vertical shaft, 
with the cistern by which it is sup- 
plied with water; to this is also attached 
what is denominated the lighter, which is jj-jp 
intended to relieve the lower gudgeon jjJB 
and step from the pressure of the column lljp 
of water, and also, when desired, the fj|| 
weight of the wheel, and whatever is at- 
tached thereto. The whole being shown in a vertical sec- 
tion through the axis of the wheel. 

"A A is the cistern of water, the construction of which, 
with its penstock, may be seen at B A, fig. 4. 

" D the wheel, the flanch on its upper side, passing 
within the edge of that on the lower plate of the cistern. 

"LL the lighter for relieving the gudgeon and step of 
the shaft and wheel from the downward pressure. 



396 



APPENDIX. 



"The lighter is a circular plate of iron, concentric 
with the wheel, and attached to the same shaft. Upon 
its lower side is a flanch, or projecting rim, fitting into 
an orifice in the upper plate of the cistern, in the same 
manner in which that of the wheel fits into the lower 
plate; allowing, therefore, of a vertical motion of the shaft 
to a certain extent, without binding upon the plates of 
the cistern. 

"From the equal pressure of fluids in all directions, 
the lighter, (when equal in its area to that of the orifice 
of the wheel,) will be pressed upwards with the same de- 
gree of force with which the latter, (the wheel,) is pressed 
downwards; and if made larger, it will be pressed up- 
wards with a greater force; and may be so proportioned 
as to take off the weight both of the machinery and of the 
water, from the gudgeon and its step. 

"When a single wheel is placed upon a horizontal 
shaft, the lighter will take the place of the second wheel, 
and so also in the case of any odd number of wheels, 
either on a vertical or horizontal shaft. 

" Fig. 4 represents the Figure 4. 

double reacting wheel on 
a vertical shaft. A being 
the penstock — B the cis- 
tern — DD the wheels, re- 
volving within the plates CP 
of the cistern in the sameM 
manner as the wheel and 




lighter in fig. 3. 

"The upper wheel in 
this arrangement answers 
all the purposes of the 
lighter in the former, the 
orifice of which may be enlarged, if desired, with the 
same views." 

The foregoing is a description of the reaction wheel, 
as patented by Mr. Calvin Wing, and is given in the lan- 
guage of his specification; it exhibits, therefore, his views 
upon the subject. The buckets are sometimes so made as 
not to lap, the inner end of one terminating in a line with 
the outer end of another. Some persons construct them 



APPENDIX. 397 

so that the buckets are adjustable, thus allowing the aper- 
tures to be enlarged or diminished, according to the quan- 
tity of water, employed, or of machinery to be driven. 
There are in fact, not fewer, we believe, than eight or 
ten patents for different modifications of this wheel, and 
from the interest which it has excited, it may be con- 
sidered as in a fair way to have its relative merits fully 
tested." * 



EXPLANATION, &C. 399 



Explanation of the Technical Terms, fyc, used in the Work. 

Aperture — The opening by which water issues. 

Area — Plain surface, superficial contents. 

Algebraic signs used are : -f for more, or addition ; — less, subtracted ; 
X multiplication; -j- division; = equality; ^/ the square root of; 
86 2 for 86 squared ; 88 3 for 88 cubed. 

jBiquadrate — A number squared, and the square multiplied into itself 
— the biquadrate of 2 is 1 6. 

Corollary — Inference. 

Cuboch — A name for the unit or integer of a power, being the effect 
produced by one cubic foot of water in one foot perpendicular descent. 

Cubic foot of waler — What a vessel one foot square and one foot deep 
will hold. 

Cube of number — The product of a number multiplied by itself twice. 

Cube root of a number — say of 8; — the number which multiplied into 
itself twice will produce 8 ; namely 2. Or, it is that number by 
which, if you divide a number twice, the quotient will be equal to 
itself. 

Decimal point — set at the left hand of a figure, shows the whole num- 
ber to be divided into tens, as ,5 for t 5 q ths ; ,57 for T 5 7 ¥ ths; ,557 for 

iWo ths P arts -_ m 
Equilibrio, Equilibrium — Equipoise or balance of weight. 

Elastic — Springy. 

Friction — The act of rubbing together. 

Gravity — The tendency all matter has to fall downwards. 

Hydrostatics — The science which treats of the weight of fluids. 

Hydraulics — The science which treats of the motion of fluids, as in 

pumps, water-works, &c. 
Impulse — Force communicated by stroke, or other power. 
Impetus — Violent effort of a body inclining to move. 
Momentum — The force of a body in motion. 
Maximum — Greatest possible. 
Non- elastic — "Without spring. 
Octuple — Eight times told. 

Paradox — Contrary to received opinion : an apparent contradiction. 
Percussion — Striking together, impact. 
Problem — A question proposed. 
Quadruple — Four times, fourfold. 



400 EXPLANATION, &C. 

Radius — Half the diameter of a circle. 
Bight Angle — a line square, or perpendicular to another. 
Squared — Multiplied into itself; 2 squared is 4. 
Theory — Speculative plan existing only in the mind. 
Tangent — A line perpendicular to, or square with, a radius, and touch- 
ing the periphery of a circle. 
Theorem — Position laid down as an acknowledged truth. A rule. 
Velocity — Swiftness of motion. 
Virtual or effective descent ofivater — (See Article 61.) 



SCALE FROM WHICH THE FIGURES ARE DRAWN IN 
THE PLATE FROM II. TO XI. 

Plate II. Fig. 11, 12, 8 feet to an inch; fig. 19, 10 feet to an inch. 

III. Fig. 19, 20, 23, 26, 10 feet to an inch. 

IV. Fig. 28, 29, 30, 31, 32, 33, 10 feet to an inch, 

VI. Fig. l,10feettoaninch;fig.2,3,8,9,10,ll,2feettoaninch. 
VII. Fig. 12, 13, 14, 15, 2 feet to an inch; fig. 16, 10 feet to an inch; 
X. Fig. 1,2, 18 feet to an inch; fig. H. 1, in fig. 1,4 feet to an inch^ 
XL Fig. 1, 2, 3, 2 feet to an inch; fig. 6, 8, 1 foot to an inch. 



THE END. 






Plalv.l 




H.-.i.ll 




rirtu-.in 




HatcJV 




22 '-'*» 




! ■.■.•'. , -.1 'Be 



Plate. VI. 




Jlvahl aJ> 



Plate AH I 




Hat e Yltt. tflfSM 




PlateJC 




Plate.XE 




Plate.™. 




Plat* XJV. 




Plate. XV 




Plate. XVI. 




" 



Plafe.XVH 




Plate XVIII 



lllllll llillllllll 






t* 










- 


















































3 














































- 









J-ff/.J. 




;;.. . -. ; 



ELa±e . X J X 




Plate XXI . 





-^ 



Plate XXII. 




Plate XXIV 




r i, xxv 1 1 

P i,n r l; BO l 1,1, 




t~m 




I 



m 



!Xl 



mm TO 



5 






m#$n 



j 

j 



7 



rL 









CATALOGUE 

OF 

LEA * BLANCHARD'S 

PUBLICATIONS. 

NEW AND REVISED EDITION. NOW READY. 

LYNCH'S DEAD SEA EXPEDITION. 



NARRATIVE OF THE UNITED STATES EXPEDITION 

TO THE RIVER JORDAN AND THE DEAD SEA. 
BY W, F. LYNCH, U. S. N., 

Commander of the Expedition. 

In one large and beautiful octavo volume, of over five hundred pages. 

With Maps and Numerous Illustrations, executed in the handsomest style, 

LIST OF ILLUSTKATIONS. 

MAPS. 

Sketch Map of the River Jordan, ? rv i 1 * A 

Sketch Map of the Dead Sea, j 0n a lar S e scale > from accurate surve ^ 

TWENTY-EIGHT PLATES, BEAUTIFULLY EXECUTED ON WOOD. 



A Ta'amirah. 

Miistafa the Cook. 

Masada. 

Christian Arabs of Kerak. 

Sheikh of Mezra'a. 

Wady Mojeb. 

Greek Archbishop. 

Tomb of Absalom. 

Garden of G-ethsemane. 

Tombs in the Valley of Jehoshaphat 

Greek Priest* at Nazareth. 

Fountain of Nazareth. 

Great Sheikh of the 'Anazeh Tribes. 

Baalbec. 



Source of the Jordan. 

Camp on the River Belus. 

'Akil Aga. 

Sherif of Mecca. 

Caravan of the Expedition. 

Tiberias. 

Ruined Bridge of Semakh. 

Jum'ah. 

View on the Jordan. 

Sherif Massa'd, Emir Nassir, and Beni 

Sukr Sheikh. 
Pilgrims Bathing in the Jordan. 
Shore of the Dead Sea. 
Ain Jidy. 
Pillar of Salt. 

CONTENTS. 

Chapter I. — Introduction. II. — From New York to Port Mahon. III. — From Part Mahon ta> 
Smyrna. IV. — From Smyrna to Constantinople. V. — Constantinople and Voyage to Syria. VI. — 
From Beirut to departure from St. Jean D'Acre. VII. — From St. Jean D'Acre to departure from 
the Sea of Galilee. VIII.— From the Sea of Galilee to the Falls of Buk'ah. IX.— From the Falle 
of Buk'ah to the Fourth Camping Place on the Jordan. X. — From the Fourth Camp on the Jordan 
to the Ford of Scka\ XI. — From the Ford of Scka" to Pilgrim's Ford. XII. — From Pilgrim's 
Ford to First Camp on the Dead Sea. XIII. — From Ain el Teshkhah to Ain Jidy (Engaddi.) 
XIV. — Expedition around the Southern Sea. XV. — Excursion to Masada. XVI. — From Camp to 
the Capital of Moab. XVII. — Cruise along the Arabian Shore. XVIII. — From the Outlet of the 
Hot Springs of Callirhoe to Ain Turabeh. XIX. — From the Dead Sea to the Conventof Mar Saba. 
XX. — From Mar Saba to Jerusalem. XXI. — Jerusalem. XXII. — From Jerusalem to Jaffa. 
XXIII. — From Jaffa to Nazareth. XXIV. — From Nazareth to the Source of the Jordan. XXV. — 
From the Source of the Jordan to Damascus, Ba'albek, Beirut, and Home. 

From this summary of the Contents, it will be seen that the Expedition explored all of the most 
interesting spots of the Holy Land. They were examined with great care, especially those of 
which there is little or no authentic information ; and the results will be found embodied in this 
volume. As the official account of an expedition which has attracted no small share of public atten- 
tion, it has much interest for the general reader, while to the biblical student it will be necessary 
for the proper understanding of the Geography of the Holy Land. As a work of art, too, it merits 
attention; neither care nor expense has been spared to render it worthy its national character. 
It is printed on large type and fine paper; the illustrations are very numerous, presenting the 
most interesting points connected with the Expedition, and have been engraved in the best style 
of the art ; and the whole may confidently be presented as equal, if not superior, to any original 
work of the kind as yet attempted in this country. 



LEA & BLANCHARD'S NEW PUBLICATIONS. 



LYNCH' S DEAD 

This book, so long and anxiously expected, 
fully sustains the hopes of the most sanguine and 
fastidious. It is truly a magnificent work. The 
type, paper, binding, style, and execution, are 
all of the best and highest character, as are also 
the maps and engravings. It will do more to ele- 
vate the character of our national literature than 
any work that has appeared for years. The in- 
trinsic interest of the subject will give it popu- 
larity and immortality at once. It must be read 
to be appreciated ; and it will be read extensive- 
ly, and valued, both in this and other countries. 
— Lady's Book, August, 1849. 

Lieut. Lynch's book must be pronounced of 
great value, not only for the additions which it 
makes to our knowledge, but as the authentic re- 
cord of an enterprise in the highest degree honora- 
ble to all the parties concerned. In our esteem the 
value of the work is greatly enhanced by the en- 
gravings. The interest of these lies in their re- 
presenting subjects mostly new to those who have 
been wearied with the five hundreth repetition 
of the same scenes and objects. The views on the 
Dead Sea are of special and remarkable interest, 
and the costume figures are also striking and sug- 
gestive. — North British Review, August, 1849. 

A large and elegant volume of marked interest 
and of decided value. The Expedition, as our 
readers are aware, was conducted under the 
Authority of the United States, and resulted in a 
much more satisfactory exploration of the region 
visited than had ever before been made. The 
book is very handsomely printed, and contains 
numerous spirited pictorial illustrations. — N. Y. 
Courier and Enquirer. 

A most elegant volume of 500 pages, profusely 
illustrated with beautiful plates and maps. The 
style of the work is at once simple and capti- 
vating, possessing all the interest of a romance 
as well as the sterling excellence of a reliable 
statement of facts. It is worthy to be ranked 
with Layard's great work on Nineveh. — Phila. 
Evening Bulletin. 

The present volume is a well-written narra- 
tive, filled with lively and interesting descriptions 
of the country and the people, and the remark- 
able scenes and incidents he met with, besides 
having the merit of being a reliable work in all 
its statements. This volume, we are satisfied, 
will be much sought after. — Phila. Ledger. 

When, however, he fairly " gets under weigh," 
every page possesses interest, and we follow him 
with eagerness in his perilous and tortuous voy- 
age down the Jordan, and his explorations of the 
mysterious sea, upon which the curse of the Al- 
mighty visibly rests. His privations, toils, and 
dangers were numerous, but were rewarded by 
success where all others had failed. He has con- 
tributed materially to our knowledge of scriptural 
geography, particularly in his charts of the Jordan 
and Dead Sea, which he fully explored. If our 
readers wish to know all he has done, they must 
procure and read his book; we cannot give even 
an outline of it. We can only add, that the pub- 
lishers have done their full duty in their depart- 
ment, and the maps and plates are all that could 
be desired. — Presbyterian. 

It is splendidly got up, and constitutes one of 
the most useful and deeply interesting volumes 
that has recently been issued from the press. It 
is running over with graphic pictures for the 
poet, stirring adventure for the common reader, 



SEA. ( Continued.) 

and deep science of philosophy for the student. 
It will at once add greatly to the knowledge of 
the interesting regions explored, and to the well- 
earned fame of the accomplished author. It will 
soon find a place in every well-selected library 
in the country. — Albany Evening Journal. 

The maps alone, drawn as they are from actual 
survey, and changing as they do all our previous 
ideas of the course of the Jordan and the con- 
figuration of the Dead Sea — are an ample return 
for the trouble and expense of the Expedition. 
Messrs. Lea & Blanchard deserve the thank3 
of the reading world for the splendid style in 
which the work is executed. Maps, engravings, 
type, paper, and printing, are all in first-rate 
style — all worthy of a national work. — Scott's 
Weekly Paper. 

The publication of this work has been looked 
for with so much interest, that we expect to 
gratify many readers by giving it an extended 
notice. Indeed, the intrinsic merits of the work 
claim for it mote than ordinary attention and ex- 
amination. The scene of exploration is hallowed 
by historic associations, and possesses other and 
peculiar features of interest, and it is quite natural 
that every intelligent Christian and philanthropist 
should await with eager curiosity, a narrative of 
personal observation of the present appearance 
of those interesting localities. Such a one will 
be glad of the assurance, that in Lieut. Lynch's 
book he will find a succinct, direct, pleasing ac- 
count of those scenes which, under shelter of 
our national flag, he successfully explored. 

The record he has given of the scenes through 
which they passed will be eagerly perused by 
his countrymen, and will be a lasting memorial 
of a great national enterprise skilfully consum- 
mated. — JV. Y. Commercial Advertiser. 

Lieut. Lynch, the commander, entered upon 
the service with a degree of enthusiasm which 
foretokened the complete success he has at- 
tained; and the work he has given to the public 
is among the most valuable of the results of his 
enterprise and efforts. It is a lively, spirited, 
agreeable description of the various objects he 
saw, and conveys a vivid idea of many of the 
most interesting scenes, which, to the Christian 
mind, the world can offer. The work is embel- 
lished by numerous and well-executed maps and 
engravings. — North American. 

In the work before us, he describes, in an easy, 
flowing, yet graphic style, the progress of his 
voyage, the various places visited, and many 
scenes and objects of great interest, which came 
under his observation in his journeyings in the 
Land of Israel and Moab, as well as the various 
phenomena of the River and Sea, which he was 
sent to explore. — The various information which 
the intelligent reader will derive from it, will am- 
ply reward him for a perusal. — Christian Observer. • 

This is a work that well deserves to be exten- 
sively read. It is not only interesting from the 
sacred associations connected with the scenes 
which it so graphically describes, but also from 
the familiar and unaffected style of its narrative. 
It is a work that should find a place in every 
library, and we commend it to the perusal of the 
public with the utmost confidence, that they will 
consider the time well spent that is bestowed 
upon its pages. It is printed in a style of beauty 
and excellence that makes it additionally attrac- 
tive. — Charleston Mercury. 



MISS MARTI NEAU'S NEW WORK. 



EASTERN LIFE, PRESENT AND PAST, 
BY HARRIET MARTINEAU. 

In.Qne Handsome Crown Octavo Volume. 



LEA & BLANCHARD'S NEW PUBLICATIONS. 



MAGNIFICENT PRESENTATION WORK. 
Mow Ready. 

IRISH MELODIES, 

BY THOMAS MOORE, Esq. 
"With Notes and Autobiographical Prefaces. 

ILLUSTRATED WITH BEAUTIFUL STEEL PLATES, 

ENGRAVED UNDER THE IMMEDIATE SUPERINTENDENCE OF MR. EDWARD FINDEN. 

In one large imperial 4to. volume of 174 pages, handsomely bound in extra cloth, with gilt edges. 

BEAUTIFULLY PRINTED ON SUPERIOR PAPER. 

LIST OF PLATES. 

Nora Creina, ------ Painted by W. P. Frith, Engraved by E. Finden. 

Rich and Rare were the Gems she Wore, " W. Fisher, " W. H. Mote. 

Eveleen, " R. T. Bott, " E. Finden. 

Love : s Young Dream, ----- "A. Derby, " E. Finden. 

Lesbia, " W. P. Frith, " W. Holl. 

Kathleen and St. Kevin, - " E. Hawkes, « W. Holl. 

The Hamlet's Pride, - " W. Room, " W. Edwards. 

Laughing Eyes, ----- " W. P. Frith, " E. Finden. 

The Mountain Sprite, - - - - " F. Wood, " E. Finden. 

The Desmond's Love, - " F.Crowley, " W.Edwards. 

The care which has been exercised in every portion of this volume, both as to its mechanical and artisti- 
cal execution, renders it in all respects well worthy of the '-Irish Melodies." In illustrations, type, printing, 
paper, and binding, it is equal to anything that has as yet appeared in this country ; and as a work whose at 
traction is not confined to a single season, it should command the attention of the public. 



Now Ready— INGBRSOLL'S NEW "WORK. 

HISTORICAL SKETCHTf THE SECOND WAR 
BETWEEN THE UNITED STATES DF AMERICA AND GREAT BRITAIN, 

DECLARED BY ACT OP CONGRESS THE 18th OP JUNE, 1812, 
AND CONCLUDED BY PEACE THE 15th OF FEBRUARY, 1S15. 

BY CHARLES J. INGERSOLL. 

EMBRACING THE EVENTS OF 1814. 

In one well-printed 8vo. Volume of 318 pages, double columns, paper covers, price One Dollar. 

Persons residing in the country can obtain this book, through the Post-Office, by a remittance of One 

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KENNEDY'S LIFE OF WIRT. 



MEMOIRS OF THE LIFE OF WILLIAM WIRT, 

BY JOHN P. KENNEDY. 

NEW EDITION, REVISED. 
In two large vols., royal 12mo., with a Portrait and fac-simile letter from John Adams. 

The whole of Mr. Wirt's Papers, Correspondence, Diaries, &c, having been placed in the hands of Mr. 
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history of the times, as well as to the private life of Mr. Wirt. 

The favorable manner in which this work has been everywhere received, having rapidly exhausted the 
first edition, the publishers have pleasure in presenting a second, with revisions by the author, in a smaller 
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the intrinsic merit of the volumes, which have elicited the universal approbation of the press. From among 
numerous recommendations a few are submitted. 

One of the most valuable books of the season, and certainly one of the most entertaining works ever pub- 
lished in this country. Mr. Kennedy is admirably qualified for the preparation of such a work, and has evi- 
dently had access to a great variety of useful material. The work is one which should be in the hands of 
every young man in the country. Its intrinsic interest will secure it a very general popularity. — N. Y. Cou- 
rier and Enquirer. 

The genius of the author and the popular character of his subject insure an equally interesting and valua- 
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and embellished with a mezzotint likeness of Mr. Wirt from a portrait by Charles B. King — Philadelphia 
North American. 

The fascinating letters of Mr. Wirt, one of the most brilliant and agreeable men of the day, in themselves 
furnish a rich fund of instruction and enjoyment.— Richmond Inquirer. 

This work has been looked for with much interest by the public, and will not disappoint the high expecta- 
tions justly based upon the well-known talents of the author, and the abundant materials left by the distin- 
guished orator and jurist, to which he has had free access. — Baltimore American. 

The style is at once vigorous and fascinating, and the interest of the most absorbing character. — Philadel- 
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The publishers have great pleasure in presenting: to the public this work in a complete form. During the 
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THE WESTERN WORLD; 

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The attempt of the authoress is educational, but the qualities of her researches are so laboured, and the in- 
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Now Ready. JOHNSTON'S PHYSICAL ATLAS. 

THE PHYSICAL ATLAS 

OF NATURAL PHENOMENA. 

FOR THE USE OF COLLEGES, ACADEMIES, AND FAMILIES, 

BY ALEXANDER KEITH JOHNSTON, F. R. G. S., F. G. S., 

Geographer at Edinburgh in Ordinary to her Majesty, Honorary Member of the Geographical Society, Berlin. 
In one large volume, imperial quarto, handsomely bound, 

With Twenty-six Plates, Engraved and Colored in the best style. 

Together with 112 pages of Descriptive Letter-press, and a very copious Index. 
LIST OF PLATES. 



GEOLOGY. 

1. Geological Structure of the Globe. 

2. Mountain Chains of Europe and Asia. 

3. Mountain Chains of America. 

4. Illustration of the Glacier System of the Alps. 

(Mont Blanc.) 

5. Phenomena of Volcanic Action. Palaeontological 

and Geological Map of the British Islands. (Front- 
ispiece.) 



HYDROGRAPHY. 

1. Physical Chart of the Atlantic Ocean. 

2. Physical Chart of the Indian Ocean. 

3. Physical Chart of the Pacific Ocean or Great Sea. 

4. Tidal Chart of the British Seas. 

5. The River Systems of Europe and Asia. 

6. The River Systems of America. 
Tidal Chart of the World. 



METEOROLOGY. 

1. Humboldt's System of Isothermal Lines. 

2. Geographical Distribution of the Currents of Air. 

3. Hyetographic, or Rain Map of the World. 

4. Hyetographic, or Rain Map of Europe. 



NATURAL HISTORY. 

1. Geographical Distribution of Plants. 

2. Geographical Distribution of the Cultivated Plants 
used as Food. 

3. Geographical Distribution of Quadrumana, Eden- 
tata, Marsupialia, and Pachydermata. 

4. Geographical Distribution of Carnivora. 

5. Geographical Distribution of Rodentia and Rumi- 
nantia. 

Geographical Distribution of Birds. 

7. Geographical Distribution of Reptiles. 

8. Ethnographic Map of the World. 

9. Ethnographic Map of Great Britain and Ireland. 

This very conviction of its value would lead us to urge upon Mr. Johnston the expediency of some reduced 
form of his great Atlas, which might render it more accessible to common readers. * * We know of no work 
of which the methods are so well fitted for the instruction of those who come ignorantly to the subject. — 
Quarterly Review. 

To the scholar, to the student, and to the already large, yet daily increasing multitude of inquirers who 
cultivate natural science, the Physical Atlas is a treasure of incalculable value. It brings before the mind's 
eye,inone grand panoramic view, and in a form clear, definite, and easily comprehensible, all the facts at 
present known relative to the great subjects of which it treats, and may be regarded as a lucid epitome of a 
thousand scattered volumes, more or less intrinsically valuable, of which it contains the heart and substance. 
— Blackwoo&s Magazine. 

By devoting a single hour to the contemplation of our globe in the diorama of a Physical Atlas, the student 
will witness the grandeur of the tenement in which he dwells, and will not fail to appreciate the beautiful 
conception of Humboldt, when he speaks of " the life of the earth."— North British Review. 

The author avails herself, with much pleasure, of an opportunity of expressing her admiration of the accu- 
racy, extent, and execution of Mr. Keith Johnston's Physical Atlas, and of the valuable information contained 
' ii the letter-press which accompanies it, which has afforded her the greatest assistance. — From the Neiv Edi- 
ion of Mrs. SomervilWs Physical Geography . 



SOMERYILLE'S PHYSICAL GEOGRAPHY— New and Improved Edition— Now Ready. 

physical Geography. 

BY MARY SOMERVILLE, 

AUTHOR OF "THE CONNECTION OF THE PHYSICAL SCIENCES," ETC. ETC. 

SECOND AMERICAN EDITION, 
From the Second and Revised JJondon Edition* 

WITH AMERICAN NOTES, GLOSSARY, &c. 
In one neat royal 12mo. vol., extra cloth. 

The great success of this work, and its introduction into many of the higher schools and academies, have 
induced the publishers to prepare a new and much improved edition. In addition to the corrections and im- 
provements of the author bestowed on the work in its passage through the press a second time in London, 
notes have been introduced to adapt it more fully to the physical geography of this country; and a comprehensive 
glossary has been added, rendering the volume more particularly suited to educational purposes. The 
amount of these additions may be understood from the fact that not only has the size of the page been increased, 
but also the volume has been enlarged by over one hundred and fifty pages. 

The present work is of the mvltum in parvo class, giving within convenient compass an admirable sum- 
mary of the geography, topography, and natural history of the four great continents of the earth. We know 
of few books, if any, which contain so much information of a valuable kind in an available form. The 
author possesses, in a remarkable degree, the power of condensing and lucidly stating her facts and infer- 
ences. — N. Y. Commercial Advertiser. 



jvow sjEJinir. 



ATLAS TO "DANA ON ZOOPHYTES." 

Being Volume IX. of the Publications of the United States Exploring Expedition. 
Large imperial folio, with sixty-one plates, drawn and colored after nature. 
Of this magnificent work, equal to anything of the kind which has been produced in Europe, but very few 
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ASPECTS OF NATURE, 

IN DIFFERENT LANDS AND DIFFERENT CLIMATES. 

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Traces our literary history with remarkable zest, fairness, and intelligence.— JV. Y. Home Journal. 



ZOOLOGICAL RECREATIONS-Just Issued. 

BY W. J. BR0DER1P, ESQ., F.R.S., ETC. 

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This is one of those delightful books which are made up of description, narrative, and sentiment all mingled 
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THE EARLIEST TIMES TO THE REIGN OF KING GEORGE U. 
BY JOHN LORD CAMPBELL, A. M., F. R. S. E. 

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enough to possess it. — Frazer's Magazine. 

A work which will take its place in our libraries as one of the most brilliant and valuable contributions to 
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FRANCE UNDER LOUIS PHILIPPE. 



THE HISTORY OF TEN YEARS, 1830—1840: 
OR, FRANCE UNDER LOUIS PHILIPPE. 

BY LOUIS BLANC, 

Secretary to the Provisional Government of 1848. 

Tkanslated by WALTER K. KELLY. 

In two handsome crown octavo volumes, extra cloth, or six parts, paper, at fifty cents. 

This is a remarkable work. The ten years, 1830-1840. were troubled, stirring, and important times to every 
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the subjects of immense interest to all readers — the style unusually excellent. — Foreign Quarterly Review. 



HISTORY OF THE FRENCH REVOLUTION OF 1789. 

BY LOUIS BLANC, 

Author of " France under Louis Philippe," &c. 

TRANSLATED FROM THE FRENCH. 

In one volume, crown octavo. 



STEIMETZ'S HISTORY OF THE JESUITS. 

HISTORY OF~THE JESUITS. 

FROM THE FOUNDATION OF THEIR SOCIETY TO ITS SUP- 
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THEIR MISSIONS THROUGHOUT THE WORLD; THEIR EDUCATIONAL SYSTEM AND 
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By ANDREW STEINMETZ, 

Author of "The Novitiate." and " The Jesuit in the Family." 
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HERVEY'S COURT_OF GEORGE II. 

MEMOIRS OF THE REM OF GEORGE THE SECOND, 

FROM HIS ACCESSION 

TO THE DEATH OF QUEEN CAROLINE. 

BY JOHN LORD HBRVBY. 

EDITED, FROM THE ORIGINAL MANUSCRIPT, AT ICKWORTH, 

By the Right Honorable JOHN WILSON CROKER, LL. D., F. R. S., &c. 

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LIBRARY OF ILLUSTRATED SCIENTIFIC WORKS. 

UNDER THIS TITLE LEA & BLANCHARD ARE PUBLISHING 

A SERIES OF BEAUTIFULLY ILLUSTRATED WORKS, 

ON VARIOUS BRANCHES OF SCIENCE, 

BY THE MOST DISTINGUISHED MEN IN THEIR RESPECTIVE DEPARTMENTS. 

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have appeared in this country. 

Specimens of the Engravings and style of the volumes may be had on application to the publishers. 
MULLER'S FHYSICS-LATELY ISSUED. 

P R I N CI P L E S 

OF 

PHYSICS AND METEOROLOGY. 

BY PROFESSOR J. MULLER, M. D. 

EDITED, WITH ADDITIONS, BY R. EGLESFELD GRIFFITH, M. D. 
In one large and handsome octavo volume, with 550 wood-cuts, and two colored plates. 

This is a book of no ordinary or ephemeral value. It is one of a series, now republishing in London, on the 
different branches of science, which, from its thorough character and extended range, is much needed in 
this country. Its design is to render more easily accessible an extensive knowledge of the general principles 
of physics and meteorology ; and the distinguished author has certainly realized the design to a wonderful 
extent. The subjects treated upon are very numerous — statics, hydrostatics, dynamics, hydrodynamics, pneu- 
matics, the laws of the motions of waves in general, sound, the theory of musical notes, the voice and hearing, 
geometrical and physical optics, magnetism, electricity and galvanism, in all their subdivisions, heat and 
meteorology. The size is nevertheless convenient— one handsome octavo volume, of six hundred pages — 
in clear, bold type, and profusely illustrated. In the execution of the illustrations we have rarely seen any 
thing equal to this American edition. — JV. Y. Commercial. 

This is a large, elegant, and most admirable volume — the first of a series of scientific books now passing 
through the press in London, and which cannot fail to commend themselves to the favor of all who take any 
interest in the progress of science among the great mass of the people. The author is one of the most distin- 
guished scientific men in Germany, and these works have been prepared with the utmost care, and are put 
forth in a form admirably adapted to secure that wide circulation and universal favor which they deserve. — 
JV. Y. Courier and Inquirer. 

The Physics of Muller is a work superb, complete, unique : the greatest want known to English Science 
could not have been better supplied. The work is of surpassing interest. The value of this contribution to 
the scientific records of this country may be duly estimated by the fact that the cost of the original drawings 
and engravings alone has exceeded the sum of £2,000.— Lancet. 

A work of which all parties may be proud. — Colonization Herald. 

An excellent work, fully and elegantly illustrated. — Silliman's Journal. 

From Professor Renwick, of Princeton University. 

I have been much gratified with the style in which the work is got up. It is not only highly creditable to 
the publishers, in comparison with other American books of a similar character, but will stand on an equality 
with the best foreign editions. 

From Professor W. H. Bartlett, XT. S. Military Academy, West Point. 

I deem this work a most valuable addition to the educational facilities of the country, and a rich source of 
information to the general reader, as it is truly an elegant specimen of typography. 

NOW READY. 

PRACTICAL PHARMACY. 

COMPRISING THE ARRANGEMENTS, APPARATUS, AND MANIPULATIONS OF THE 
PHARMACEUTICAL SHOP AND LABORATORY. 

BY FRANCIS MOHR, Ph. D., 

Assessor Pharmaciee of the Royal Prussian College of Medicine, Coblentz; 

AND THEOPHILUS REDWOOD, 

Professor of Pharmacy in the Pharmaceutical Society of Great Britain. 

EDITED, WITH EXTENSIVE ADDITIONS, 

BY PROFESSOR WILLIAM PROCTER, 

Of the Philadelphia College of Pharmacy. 
In one handsomely printed octavo volume, of 570 pages, with over 500 engravings on wood. 

Such a manual as the work before us has long been a desideratum in this country. There has been a great 
want of a proper text-book of Pharmacy, and to this want may be attributed much of the ignorance which 
prevails on this subject, in places remote from the large cities. The minute practical instruction which it 
.conveys, will introduce a new era in the shop of the apothecary throughout the United States. We recom- 
mend it, in the strongest manner, to the attention of the apothecary and druggist, as well as to the physician 
who prepares his own prescriptions, as a unique compendium of valuable, practical knowledge in Pharmacy. 
— Transylvania Med. Journal, August, 1849. 

In preparation, works on JHetallurg-y, Food, the Steam Engine, Machines, Astronomy, 

Rural Economy, Kc. 



LEA & BLANCHARD'S NEW PUBLICATIONS. 



Library of Illustrated Scientific Works. {Continued.) 

KNAPP'S CHEMICAL TECHNOLOGY. 

TECH NO LOGY; 

OR, CHEMISTRY APPLIED TO THE ARTS AND TO MANUFACTURES. 
BY DR. F. KNAPP, 

Professor at the University of Giessen. 
Edited, tcilh numerous J\*otes and Additions, bi/ 

DR. EDMUND RONALDS and DR. THOMAS RICHARDSON. 
First American Edition, with Notes and Additions, 

By Professor WALTER R. JOHNSON. 

In two handsome octavo volumes, printed and illustrated in the highest style of art. 

Volume One, lately published, with two hundred and fourteen large wood engravings. 

Volume Two, now ready, with two hundred and fifty wood engravings. 

One of the best works of modern times. — New York Commercial. 

We think it will prove the most popular, as it is decidedly the best of the series. Written by one who has 
for many years studied both theoretically and practically the processes which he describes, the descriptions 
are precise, and conveyed in a simple unpretending style, so that they are easily understood, while they are 
sufficiently full in detail, to include within them everything necessary to the entire comprehension of the 
operations. The work is also carefully brought down to include the most recent improvements introduced 
upon the continent of Europe, and thus gives us full descriptions of processes to which reference is fre- 
quently made in other works ; while many of them are, we believe, now for the first time presented in a com- 
plete state to the English reader. — Franklin Institute Journal. 

In addition to the valuable scientific matter contained in the original work, very extensive American addi- 
tions have been made to it by the editor, which are exceedingly valuable, and of much interest to the general 
reader. The publishers have spared no pains in bringing out a work of superior mechanical execution 
and rare excellence, with numerous skilfully engraved cuts, designed to illustrate the various subjects 
treated in this work. We feel confident that, as a truly useful publication, it will be eagerly sought after and 
highly appreciated — N. Y. Farmer and Mechanic. 

We had the pleasure of noticing, in a former number, the first volume of this excellent work, and of ex- 
pressing our high sense of its value. We need say little more, therefore, of its continuation, than that it fully 
sustains the character of its predecessor, both in regard to ihe value of the original treatise, and the number 
and importance of the additions which have been made to it by the English editors. — The British and 
Foreign Medico- Chirurgical Review. 

When we say that this volume begins another of the superb "Library of Illustrated Books," republished 
from the London series by Lea & Blanchard, of which Muller's Physics and Meteorology, and Weisbach's 
Mechanics and Engineering (the first volume of the latter), have already appeared ; that the present work is 
on a subject coming home to the business and bosoms, because to the economic interests of Americans ; that 
its American editor is Prof. Walter R. Johnson, who has enriched it with numerous valuable additions, the 
results of his own industrious researches in the technological sciences ; and that it is illustrated and printed 
in. the same superb style which marked the previous works;— we have sufficiently explained to our readers 
the value of a work which will not need any other commendation. — North American. 

No mechanic, student of chemistry, miner, or manufacturer should omit purchasing this work. It will be 
(bund useful, interesting, and instructive to all. — Pittsburgh CommercialJournal. 

"WEISBACH'S MECHANICS. 



PRINCIPLES OF THE 

MECHANICS OF MACHINERY AND ENGINEERING, 

By Professor JULIUS WEISBACH. 

TRANSLATED AND EDITED BY PROFESSOR GORDON, OF GLASGOW. 

First American Edition, with Additions 

By Professor WALTER R. JOHNSON. 

IN TWO OCTAVO VOLUMES, BEAUTIFULLY PRINTED. 

Volume One, with 550 illustrations, just issued. 

Volume Two, with 350 illustrations, now ready. 

The second volume of this work embraces the application of the Principles of Mechanics to 
Roofs, Bridges, Platform Scales, Water Powers, Dams, Water Wheels, Turbines, Water Engines, 
&c. &c. 

This work is one of the rrost interesting to mathematicians that has been laid before us for some time ; and 
we may safely term it a scientific gem. — The Builder. 

The most valuable contribution to practical science that has yet appeared in this country. — Athenceum. 

Unequalled by anything of the kind yet produced in this country— the most standard book on mechanics, 
machinery, and engineering now extant. — N. Y. Commercial. 

In every way worthy of being recommended to our readers. — Franlclin Institute Journal. 

What the "M^canique Celeste" is to the astronomer, a treasury of principles, facts, and formulae, on which 
he may draw on almost any and every occasion, that can be conceived to arise in the field either of demon- 
stration or operation. — Methodist Quarterly Review. 

From Charles H. Haswell, Esq., Engineer in Chief, IT. S. N. 

The design of the author, in supplying the instructor with a guide forteaching, and the student with an aux- 
iliary for the acquirement of the science of mechanics, has, in my opinion, been attained in a most success- 
ful manner. The illustrations, in the fullness of their construction, and in typographical execution, are 
without a parallel. It will afford me much pleasure to recommend its use to the members of the profession 
with which I am connected. 



10 



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SCHMITZ & 
VOLUME I. 

C. JUI.II C.3ESARIS 
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WITH AN INTRODUCTION, NOTES, AND A GEOGRA- 
PHICAL INDEX IN ENGLISH. 
ALSO, 

A MAP OF GAUL, AND ILLUSTRATIVE ENGRAVINGS 

In one handsome ISmo. volume of 232 pages, extra 

cloth, price 50 cents. 



ZUMPT'S CLASSICAL SERIES. 

VOLUME IV.— (Now Ready.) 

LATIN GRAMMAR. 

BY LEONHARD SCHMITZ, PH. D., F.R.S. E., 

RECTOR OF THE HIGH SCHOOL, EDINBURGH. 

In one handsome 18mo. vol. of 318 pages, neatly half 
bound, price 60 cents. 



VOLUME II. 

PUBLII VIRGILII MAROMS CARMINA. 

WITH AN INTRODUCTION AND NOTES. 

In one handsome 18mo. vol. of 438 pages, extra cloth, 

price 75 cents. 



c. 



VOLUME III. 

CRISPI SALLHSTII 

CATILINA ET JUGURTHA. 
WITH INTRODUCTION AND NOTES IN ENGLISH. 

ALSO, 

A MAP OF NUMIDIA, AND OTHER ILLUSTRATIVE 

ENGRAVINGS. 

In one handsome ISmo. vol. of 16S pages, extra cloth 

price 50 cents. 



igni 



VOLUME V.— (Now Ready.) 

Q. Curtii Rufi de Gestis Alexandri 
Libri qui Supersunt VIII. 

With a Map, Notes, Introduction, Illustrations, SfC 
In one handsome ISmo. vol., extra cloth. 

VOLUME VI -(Now Ready.) 

M, T. CICERONIS ORATIONES SELECT*. 

With Introduction and Notes. 
In one handsome 18mo. volume. 

VOLUME VII.- (Nearly Ready.) 

INTRODUCTION TO LATIN GRAMMAR. 

BY LEONHARD SCHMITZ, Ph. D., F. R. S. E., &c. 
In one handsome ISmo. volume. 



The neatness, cheapness, and accuracy of this series, logetherwith its skillful adaptation to the wants both 
of teacher and pupil, have secured for it the almost universal approbation of those to whom the volumes have 
been submitted. From among the very numerous testimonials in its favor which the publishers have re- 
ceived they append one or two. 

From Prof. A. S. Packard, Bowdoin College, Brunswick, Me., March 8, 1849. 

I cannot refrain longer from communicating to you the highly favorable impression which they have made 
upon me. I see nothing to desire in the general style of these editions. I know of no others, which for neat- 
ness and cheapness, and sufficient helps for the student, surpass them. I am exceedingly pleased with the 
good taste, clear and precise statements, and sound scholarship, which distinguish the notes. As school 
classics I regard them as models. 

From Prof. Roche, Transylvania University, Lexington, Ky., March 31, 1849. 

Whatever influence my position may give me, shall be most cheerfully employed in bringing into general 
use. in the West these very valuable works. I trust that you will prosecute to a close the proposed series, 
and that the execution of those that remain to complete a Latin Curriculum may be as neat and in all re- 
spects as unexceptionable as that of those already published. 



BOLMAR'S FRENCH SERIES. 

New editions of the following works, by A. Bolmar, forming, in connection with "Bolmar's Levizac," a 

complete series for the acquisition of the French language: — 

A SELECTION OF ONE HUNDRED PERRIN'S FABLES, accompanied by a Key, containing the text, 
a literal and free translation, arranged in such a manner as to point out the difference between the French 
and English idiom, &c, in one vol. 12mo. 

A COLLECTION OF COLLOQUIAL PHRASES, on every topic necessary to maintain conversa- 
tion. Arranged under different heads, with numerous remarks on the peculiar pronunciation and uses of 
various words ; the whole so disposed as considerably to facilitate the acquisition of a correct pronuncia- 
tion of the French, in one vol. ISmo. 

EES AVENTURE3 DE TELEMAQUE, PAR FENELON, in one vol. 12mo., accompanied by a Key to 
the first eight books, in one vol. 12mo.. containing, like the Fables, the text, a literal and free translation, 
intended as a sequel to the Fables. Either volume sold separately. 

ALL THE FRENCH VERBS, both regular and irregular, in a small volume. 



HERSCHEL'S OUTLINES OF ASTRONOMY. (Now ready.) In one handsome volume, crown 8vo., 

with six plates and numerous wood-cuts. 
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BREWSTER'S ELEMENTS OF OPTICS. In one vol. 12mo., half bound, with many wood-cuts. 
MULLER'S PRINCIPLES OF PHYSICS AND METEOROLOGY. In one large and handsome 8vo 

volume, with 540 wood-cuts and two colored plates. 
BIRDS ELEMENTS OF NATURAL PHILOSOPHY. In one large and handsome royal 12mo. volume, 

with 372 wood-cuts. 
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FOWNE'S CHEMISTRY FOR STUDENTS. In one large royal 12mo. volume, with nearly two hundred 

wood-cuts. 

BUTLER'S ANCIENT ATLAS. In one 8vo. volume, half bound, with twenty-one colored quarto maps. 
BUTLER'S ANCIENT GEOGRAPHY. In one royal 12mo. volume, half bound. 

WHITE'S ELEMENTS OF UNIVERSAL HISTORY. Edited by J. S. Hart, LL. D. In one large royal 
12mo. volume, half bound. 

SOMERVILLE'S PHYSICAL GEOGRAPHY. In one royal 12mo. volume. 

SHAW'S OUTLINES OF ENGLISH LITERATURE. In one large royal 12mo. volume. 

From the Rev. W. G. T. Shedd, Professor of English Literature in the University of Vermont. 

I lake great pleasure in saying that it supplies a want that has long existed of a brief history of English 
Literature, written in the right method and spirit, to serve as an introduction to the critical study of it. I shall 
recommend the book to my classes. 

Burlington, May 18, 1849. 



LEA & BLANCHARD'S PUBLICATIONS.— {Law Books) 11 

SPENCE'S EQUITY JURISDICTION. 

VOLUME II. JUST READY, 
THE EQUITABLE JURISDICTION OF THE COURT OF CHANCERY; comprising its rise, progress, 
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cise account of the leading doctrines of the common law, and of the course of procedure in the courts of 
common law, with regard to civil rights; with an attempt to trace them to their sources; and in which the 
various alterations made by the legislature down to the present day are noticed. By George Spekce, Esq., 
one of her majesty's counsel. In two octavo volumes. Volume I., embracing the Principles, lately issued, 
with near TOO large Svo. pages. Volume II. just ready, 'with near 900 large pages. The publishers have 
ihe pleasure of announcing that the second volume of this valuable work is at length passing rapidly through 
the press, and will shortly be issued. It will contain the application of the Principles of Equity Jurispru- 
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NEW EDITION OF EAST'S REPORTS. 

REPORTS OF CASES ADJUDGED AND DETERMINED IN THE COURT OF KING'S BENCH. 
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HOLTHOUSE'S DICTIONARY. 

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WHEATON'S INTERNATIONAL LAW. 

ELEMENTS OF INTERNATIONAL LAW. By Henry Wheaton, LL. D., Minister of the 
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TAYLOR'S TOXICOLOGY. 

ON POISONS IN RELATION TO MEDICAL JURISPRUDENCE AND MEDICINE. By Al- 
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and author of "Medical Jurisprudence," &c. &c. Edited, with notes and additions, by R. 
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TAYLOR'S MEDICAL JURISPRUDENCE. 

A PRACTICAL TREATISE ON MEDICAL JURISPRUDENCE. By Alfred S. Taylor, Lec- 
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A NEW WORK ON COURTS MARTIAL. 

A TREATISE ON AMERICAN MILITARY LAW, AND THE PRACTICE OF COURTS- 
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TO THE MEDICAL PROFESSION. 

The following list embraces works on Medical and other Sciences issued by the subscribers. They are to 
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medical booksellers throughout the country. LEA & BLANCHARD, Philadelphia. 



DICTIONARIES AND JOURNALS. 

American Journal of the Medical Sciences, quar- 
terly, at $5 a year. 

Cyclopaedia of Practical Medicine, by Forbes, 
Tweedie, &c, edited by Dunglison, in 4 super 
royal volumes, 3154 double columned pages. 

Dunglison's Medical Dictionary, 7th ed., 1 vol. 
imp.8vo.,912 large pages, double columns. 

Hoblyn's Dictionary of Medical Terms, by Hays, 
1 vol. large 12mo., 402 pages, double columns. 

Medical News and Library, monthly, at $1 a year. 

ANATOMY. 

Anatomical Atlas, by Smith and Horner, large 
imp. 8vo., 650 figures. New and cheaper ed. 

Horner's Special Anatomy and Histology, 7th 
edition, 2 vols. 8vo., many cuts, 1130 pages. 

Horner's United States Dissector, 1 vol. large 
royal 12mo., many cuts, 444 pages. 

Maclise's Surgical Anatomy, Part I., 16 plates, 
imp. 4to. (To be complete in 4 parts.) 

Sharpey and Quain's Anatomy, by Leidy, 2 vols. 
8vo., 1300 pages, 511 wood-cuts. Now ready. 

Wilson's Human Anatomy, by Goddard, 4th edi- 
tion, 1 vol. 8vo., 252 wood-cuts, 580 pp. 

Wilson's Dissector, or Practical and Surgical 
Anatomy, with cuts, 1 vol. 12mo., 444 pages. 

PHYSIOLOGY. 

Carpenter's Principles of Human Physiology, by 
Clymer, 1 vol.8vo., 752 pp., over 300 illustra- 
tions, 4th edition, much improved and enlarged. 
1850. 

Carpenter's Elements, or Manual of Physiology, 
1 vol. 8vo., 566 pages, many cuts. 

Dunglison's Human Physiology, 6th edition, 2 
vols. 8vo., 1350 pages, and 370 wood-cuts. 

Harrison on the Nerves, 1 vol. 8vo., 292 pages. 

Kirkes and Paget's Physiology, 1 vol. 12mo., 
many cuts, 550 pages. 

Matteucci on the Physical Phenomena of Living 
Beings, 1 vol. 12mo., 3S8 pp., cuts. 

Roget's Outlines of Physiology, 8vo., 516 pages. 

Solly on the Brain, 1 vol. 8vo., 496 pp., 118 cuts. 

Todd and Bowman's Physiological Anatomy and 
Physiology of Man, with numerous wood-cuts. 
(Publishing in the Medical News.) 

PATH010GY. 

Abercrombie on the Stomach, 1 vol. 8vo., 320 pp. 
Abercrombie on the Brain, 1 vol. 8vo., 324 pp. 
Alison's Outlines of Pathology, &c, 8vo., 420 pp. 
Blakiston on Diseases of the Chest, 1 vol ., 384 pp. 
Bennet on the Uterus, 1 vol. 12mo., 146 pages. 
Blood and Urine Manuals, by Reese, Griffith, and 

Markwick, 1 vol. 12mo., 462 pages, 6 plates. 
Budd on the Liver, 1 vol. 8vo., 392 pages, plates 

and wood-cuts. 
Burrows on Cerebral Circulation, 1 vol. 8vo., 

216 pages, with 6 colored plates. 
Billing's Principles, 1 vol. 8vo., 304 pages. 
Bird on Urinary Deposits, 8vo., 228 pages, cuts. 
Hasse's Pathological Anatomy, 8vo., 379 pages. 
Hope on the Heart, by Pennock, a new edition, 

with plates, 1 vol. 8vo., 572 pages. 
Hughes on the Lungs and Heart, 1 vol. 12mo., 

270 pages, with a plate. 
Lallemand on Spermatorrhoea; 1 vol. 8vo., 320 pp 
Mitchell on Fevers, 1 vol. 12mo., 138 pages. 
Philip on Protracted Indigestion, 8vo., 240 pp 
Philips on Scrofula, 1 vol. 8vo., 350 pages. 
22 



Prout on the Stomach and Renal Diseases, 1 vol. 

8vo., 466 pages, colored plates. 
Ricord on Venereal, new ed., 1 vol. 8vo., 340 pp. 
Stanley on Diseases of the Bones, 1 vol. 8vo. 

(Now ready.) 
Vb'gel's Pathological Anatomy of the Human 

Body, 1 vol. 8vo., 536 pages, col. plates. 
Walshe on the Lungs, 1 vol. 12mo., 310 pages. 
Wilson on the Skin, 1 vol. Svo., new ed., 440 pp. 

Same work, with colored plates. 
Whitehead on Sterility and Abortion, 1 vol. 8vo., 

368 pages. 
Williams' Principles of Medicine, by Clymer, 2d 

edition, 440 pages, 1 vol. 8vo. 
Williams on the Respiratory Organs, by Clymer, 

1 vol. 8vo., 500 pages. 

PRACTICE OF MEDICINE. 

Ashwell on Females, 2d ed., 1 vol. 8vo., 520 pp. 
Bartlett on Fevers, 2d edition, 550 pages. 
Benedict's Compendium of Chapman's Lectures, 

1 vol. 8vo., 258 pages. 
Chapman on Fevers, Gout, Dropsy, &c. &c, 1 vol. 

8vo., 450 pages. 
Colombat de L'Isere on Females, translated and 

edited by Meigs, 1 vol. 8vo., 720 pages, cuts. 

New edition, just ready, 1850. 
Condie on the Diseases of Children, 3d edition, 

1 vol. 8vo., just ready, 1850, 704 pages. 
Churchill on the Diseases of Infancy and Child- 
hood, 1 vol. Svo., just ready, 1850, 636 pages. 

Churchill on the Diseases of Females, by Huston, 
4th edition, 1 vol. 8vo., 604 pages. 

Clymer and others on Fevers, a complete work 
in 1 vol. 8vo., 600 pages. 

Day on Old Age, 1 vol. 8vo., 226 pages. 

Dewees on Children, 9th ed., 1 vol. 8vo., 548 pp. 

Dewees on Females, 9th edition, 1 vol.8vo., 532 
pages, with plates. 

Dunglison's Practice of Medicine, 3d edition, 

2 vols. 8vo., 1500 pages. 
Esquirol on Insanity, by Hunt, 8vo., 496 pages. 
Meigs' Letters on Diseases of Females, 1 vol. 

Svo., 670 pages. A new work. 
Meigs on Certain Diseases of Infancy, 1 vol Svo. 

A new work, preparing. 
Thomson on the Sick Room, &c, 1 vol. large 

12mo., 360 pages, cuts. 
Watson's Principles and Practice of Physic, 3d 

edition by Condie, 1 vol. 8vo., 1060 large pages. 
West's Lectures on the Diseases of Infancy and 

Childhood. 1 vol. 8vo., 452 pp. (Now ready.) 

SURGERY. 

Brodie on Urinary Organs, 1 vol. 8vo., 214 pages. 

Brodie on the Joints, 1 vol. 8vo., 216 pages. 

Brodie's Lectures on Surgery, 1 vol. Svo. ,350 pp. 

Brodie's Select Surgical Works, 780 pp. 1 vol.8vo. 

Chelius' System of Surgery, by South and Norris, 
in 3 large 8vo. vols., near 2200 pages. 

Cooper on Dislocations and Fractures, 1 vol. 8vo., 
500 pages, many cuts. 

Cooper on Hernia, 1 vol. imp. 8vo., many plates. 

Cooper on the Testis and Thymus Gland, 1 vol. 
imperial 8vo., many plates. 

Cooper on the Anatomy and Diseases ofthe Breast, 
Surgical Papers, &c. &c, 1 vol. imp. Svo. , pl'ts. 

Druitt's Principles and Practice of Modern Sur- 
gery, 1 vol. 8vo., 576 pages, 193 cuts, 4th ed. 

Dufton on Deafness and Disease of the Ear, 1 vol. 
12mo., 120 pages. 

Durlacher on Corns, Bunions, &c, 12mo.,134 pp. 



LEA & BLANCHARD'S PUBLICATIONS.— {Medical Works.) 



13 



Pergusson's Practical Surgery, 1 vol. 8vo., 3d 

edition 630 pages, 274 cuts. 
Guthrie on the Bladder, 8vo., 150 pages. 
Jones' Ophthalmic Medicine and Surgery, by 

Hays, 1 vol. 12mo., 529 pp., cuts, and plates. 
Liston's Lectures on Surgery, by Mutter, 1 vol. 

8vo., 566 pages, many cuts. 
Lawrence on the Eye, by Hays, new edition, 

much improved, 863 pages, many cuts Sr plates. 
Lawrence on Ruptures, 1 vol. 8vo., 480 pages. 
Miller's Principles of Surgery, 2d edition, 1 vol. 

8vo.,538pp., 1848. 
Miller's Practice of Surgery, 1 vol.Svo., 496 pp. 
Maury's Dental Surgery, 1 vol. 8vo., 286 pages, 

many plates and cuts. 
Robertson on the Teeth, 1 vol.8vo.,230pp., pts. 
Sargent's Minor Surgery, 1 vol. royal 12mo., 380 

pages, 128 cuts. 

MATERIA MEDICA AND THERAPEUTICS. 

Christison's and Griffith's Dispensatory, 1 large 
vol. 8vo., 216 cuts, over 1000 pages. 

Dunglison's Materia Medica and Therapeutics, a 
new ed., with cuts, 2 vols. 8vo., 986 pages. 

Dunglison on New Remedies, 5th ed., 1 vol. 8vo., 
653 pages. 

De Jongh on Cod-Liver Oil, 12mo. (Now ready.) 

Ellis' Medical Formulary, 9th ed., much improv- 
ed, 1 vol. 8vo., 268 pages. 

Griffith's Universal Formulary, 1 large vol., 8vo. 
(Nearly ready.) 

Griffith's Medical Botany, a new work, 1 large 
vol. 8vo., 704 pp., with over 350 illustrations. 

Mayne's Dispensatory, 1 vol. 12mo., 330 pages. 

Mohr, Redwood, and Procter's Pharmacy, 1 vol. 
8vo., 550 pages, 506 cuts. 

Pereira's Materia Medica, by Carson, 2d ed., 2 
vols. 8vo., 1580 large pages, 300 cuts. 

Royle's Materia Medica and Therapeutics, by 
Carson, 1 vol. 8vo., 6S9 pages, many cuts. 

OBSTETRICS. 

Churchill's Theory and Practice of Midwifery, by 

Huston, 3d ed., 1 vol. Svo., 526 pp., many cuts. 
Dewees' System of Midwifery, 11th ed., 1 vol. 

Svo., 660 pages, with plates. 
Lee's Clinical Midwifery, 12mo.,238 pages. 
Meigs' Obstetrics; the Science and the Art; 1 

vol. 8vo., 6S6 pages, 121 cuts. 
Ramsbotham on Parturition, with many plates, 1 

large vol. imperial 8vo., 520 pp. 5th edition. 
Smith (Tyler) on Parturition, 1 vol., 400 pages. 

CHEMISTRY AND HYGIENE. 

Bowman's Practical Chemistry, 1 vol. 12mo., 

97 cuts, 350 pages. 
Brighamon Excitement, &c, 1 vol. 12mo., 204 pp. 
Dunglison on Human Health, 2d ed.,8vo., 464 pp. 
Fowne's Elementary Chemistry for Students, 2d 

ed., 1 vol. royal 12mo., 460 pages, many cuts. 
Gardner's Medical Chemistry, 1 vol. 12mo. 400 pp. 
Griffith's Chemistry of the Four Seasons, 1 vol. 

royal 12mo., 451 pages, many cuts. 
Knapp's Chemical Technology, by Johnson, Vol. 

I., 8vo., 504 pp., 214 large cuts 

Vol - 



MEDICAL JURISPRUDENCE, EDUCATION, &e. 

Bartlett's Philosophy of Medicine, 1 vol. 8vo., 

312 pages. 
Bartlett on Certainty in Medicine, 1 vol. small 

8vo., 84 pages. 
Dunglison's Medical Student, 2d ed.l2mo. ,312pp. 
Taylor's Medical Jurisprudence, by Griffith, 1 

vol. 8vo., 540 pages. 
Taylor on Poisons, by Griffith, 1 vol. 8vo., 688 pp. 
Traill'sMedical Jurisprudence,! vol. 8vo. ,234pp. 

NATURAL SCIENCE, &e. 

Arnott's Physics, 1 vol. 8vo., 4S4 pp., many cuts. 
Ansted's Ancient World, Popular Geology, in 1 

12mo. volume, with numerous cuts, 382 pages. 
Bird's Natural Philosophy, 1 vol. royal 12mo., 

402 pages and 372 wood-cuts. 
Brewster's Optics, I vol. 12mo. 423 pp. many cuts. 
Broderip's Zoological Recreations, 1 vol. 12mo.. 

pp. 3'6. 
Coleridge's Idea of Life, 12mo., 94 pages. 
Carpenter's Popular Vegetable Physiology, 1 vol. 

royal 12mo., many cuts. 
Dana on Zoophytes, being vol. 8 of Ex. Expedi- 
tion, royal 4to., extra cloth. 
Atlas to " Dana on Zoophytes," imp. folio, co- 
lored plates. 
Hale's Ethnography and Philology of the U. S. 

Exploring Expedition, in 1 large imp. 4to. vol, 
Herschel's Treatise on Astronomy, 1 vol. 12mo., 

417 pages, numerous plates and cuts. 
Herschel's Outlines of Astronomy, 1 vol. small 

8vo., plates and cuts. (Now ready.) 620 pp. 
Humboldt's Aspects of Nature, 1 vol. 12mo. (Now 

ready.) 476 pp. 
Johnston's Physical Atlas, 1 vol. imp. 4to., 26 

colored plates. (Now ready.) 
Kirby on Animals, plates, 1 vol. 8vo., 520 pages. 
Kirby and Spence's Entomology, 1 vol. 8vo., 600 

large pages; plates plain or colored. 
Miiller's Physics and Meteorology, 1 vol. 8vo., 

636 pp., with 540 wood-cuts and 2 col'd plates. 
Philosophy in Sport made Science in Earnest, 1 

vol. royal ISmo., 430 pages, many cuts. 
Roget's Animal and Vegetable Physiology, with 

400 cuts, 2 vols. Svo., 872 pages. 
Small Books on Great Subjects, 12 parts, done up 

in 3 handsome 12mo. volumes, extra cloth. 
Somerville's Physical Geography, 12mo., cloth, 

new and enlarged edition, now ready. 
Weisbach's Mechanics applied to Machinery and 

Engineering, Vol. 1. 8vo., 486 p. 550 wood-cuts. 

Vol. II., 8vo., 400 pp., 340 cuts. (Now ready.) 

YETERINARY MEDICINE. 

Clater and Skinner's Farrier, 1 vol . 1 2mo., 220 pp. 

Youatt's Great Work on the Horse, by Skinner, 
1 vol. 8vo., 448 pages, many cuts. 

Youatt and Clater's Cattle Doctor, 1 vol. 12mo., 
282 pages, cuts. 

Youatt on the Dog, by Lewis, 1 vol. demy 8vo., 
403 pages, beautiful plates. 

Youatt on the Pig, a new work with beautiful il- 
lustrations of all the different varieties, 12mo, 



II., 8vo., 426 pp., 246 cuts. 

Simon's Chemistry of Man, 8vo., 730 pp., plates. 

Neill and Smith's Analytical Compend of Practical Medicine, Surgery, Anatomy, Midwifery, Dis- 
eases of Women and Children, Materia Medica and Therapeutics, Physiology, Chemistry, and 
Pharmacy, with numerous illustrations, 1 vol. 12mo., 900 pages. 350 illustrations. 

MEDICAL BOOKS IN PRESS. 

Barlow's Practice of Medicine. In one vol. 8vo. (Preparing.) Golding Bird's Therapeutics. (Preparing.) 
Carpenter's Principles ol General and Comparative Physiology. In 1 large 8vo. vol., many cuts. (Prt-paring.) 
Stille's General and Special Therapeutics. In one vol Svo (Preparing.) Todd and Bowman's Physiological 
Anatomy and Physiology of Man. (Three-fourlhsofthis has been published in the Medical News and Library.) 
A complete work on the Slruclure and Diseases of the Ear. Malgaigne's Operative Surgery. In one vol. bvo. 
De La Beche's Geology, with many illustrations. A new work on Popular Medicine, one vol. Svo. A Cyclo- 
pedia of Anatomy and Physiology, based on the large work of Todd. Graham's Chemistry, by Bridges. 2d 
edition, much enlarged. One vol. 8vo., several hundred cuts. Meigs on some of the more important dis- 
eases of InfautS; (nearly ready,) and other works. 



14 



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departments' of'literature, 

PUBLISHED BY 

LEA & BLANCHARD. 



Acton's Modern Cookery, with cuts, 12mo., cl. 
American Ornithology, by Prince Charles Bona- 
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American Military Law and Practice of Courts 

Martial, by Lieut. O'Brien, U. S. A., 1 vol. 

8vo., cloth or law sheep. 
Ansted's Ancient World, or Picturesque Sketches 

of Creation, 1 vol. 12mo., numerous cuts. 
Addison on Contracts, and on Parties to Actions 

ex Contractu, a new and complete work, 1 

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Arnott's Elements of Physics, new edition, 1 

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Broderip's Zoological Recreations, 1 vol. royal 

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A Selection of One Hundred Perrin's Fables, 
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A Series of Colloquial Phrases. 

The First 8 Books of Fenelon's Telemachus. 

Key to the same. 

A Treatise on all the French Verbs, Regular 
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Butler's Atlas of Ancient Geography, 8vo., half 

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or cloth, with 372 illustrations. 
Brigham on Mental Cultivation, &c, 12mo., cloth. 
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Prout on Chemistry. 

Chalmers on the Moral Condition of Man. 

Whewell on Astronomy. 

Bell on the Hand. 

Kidd on the Physical Condition of Man. 

Buckland's Geology, 2 vols., with numerous 
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Roget, Buckland, and Kirby are sold separate. 
Bird's Calavar, or the Knight of the Conquest, 

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Boy's Treasury of Sports and Pastimes, 1 vol. 

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JVOW KErfltJt*. 

OUTLINES OF ASTRONOMY. 

BY SIR JOHN F. W. HERSCHEL, F. R. S.,&c. 
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With this, we take leave of ihis remarkable work ; which we hold to be, beyond a doubt, the greatest and 
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essential to all, that they become the manuals of the proficient as well as the text- books of the learner.— Aihe'm. 



